Is there a difference?
This may or may not satiate all the preferences set forth by the OP, but hopes to provide a descriptive answer as to whether or not there is a difference between 'on your account' and 'on account of you' which, perhaps considered at a grammatical level, yes, there is. But, the grammatical difference in relation to its meaning can also be so subtle that arguably for some, depending on their own personal experiences with the phrase, will hold the opinion that it's not any different and is therefore subjective.
This is because the former is generally used as an idiom and is an alternative form of the latter (making them inherently similar), while the latter is recognized as an English phrase which can have an idiomatic meaning when used as a preposition (and affirms them being similar) but when used as a conjunction then it can be seen as having a colloquial usage (and might stand to be different not particularly for its definitive meaning per se but more so in its usage).
How They're The Same When Used as an Idiom
This might be better understood when combining the explanations given as answers to a related question asked a number of years prior to this for, What's the meaning of "on somebody's account"? which shows how the difference in meaning is in the connotation that is both subtle and imprecise as summarized below:
Don't change your plans on my account.
Is generally understood as indicating that the person shouldn't go to any trouble on behalf of the speaker. However, it can also have the connotation that the speaker may not wish to accept a favor from the person or that the person should act for their own reason, under their own judgement.
To exaggerate the difference by adding context:
I will be running late and wouldn't want you to be late because of
me, so please don't change your plans on my account.
You can come with me if you want to but I was already planning to go
alone, so don't change your plans on my account.
When the object of this proposition is brief and animate, the alternative construction on someone's account is often used instead of on account of. If the object is a personal pronoun, that construction is more common; for example, on my account is more common than on account of me. Similarly, on that account, using that as a determiner, is more common than on account of that.
Though less common, the meaning and connotation can still be understood and considered as being the same if replaced with on account of me:
I will be running late and wouldn't want you to be late because of
me, so please don't change your plans on account of me.
Whereas it might sound more appropriate to apply inversion and say
I wouldn't want you to be late, so please don't change your plans
on account of me running late.
and
You can come with me if you want to but don't change your plans
on account of me going alone as I was already planning on it.
Since idioms generally are words or phrases whose meaning can't be understood outside of its cultural context, one might argue that similarly the connotation can't be understood the same way when taken outside the context of the speaker and their intentions. Therefore in meeting with the argument of
'on your account' is equivalent to 'for your benefit', and cannot mean
'because of you'
It may be justified by those who oppose this view and that might argue that what is 'for your benefit' has the connotation of that which exists 'because of you'. In the context of causation, in order for something to exist and be considered as a benefit to you (or for your benefit), you would need to exist to be the beneficiary.
So from a lowest common denominator standpoint, sort of speak, those that believe 'on your account' can mean 'because of you' would be of those who would have the cultural context or familiarity of using the idiom with a connotation that infers whether it be for your benefit or "for you" per se, they are both still because of you.
However, as much as this opposing view to the argument might be justified, the other opposing interpretation can also be true such that when you use the statement as a conjunction and in that context, it would prove the opposing view to be false as it would no longer be intended for use as an idiom. So as an idiom, arguably either can be right wherein it simply depends on who you ask as it applies to its idiomatic use as a preposition.
How They're Different as One Takes on a Colloquial Use
As a highlight of this article, consider the follow:
Merriam-Webster's Collegiate Dictionary defines on account of as "for the sake of, by reason of,"
The Cambridge Dictionary of American Idioms lists its meaning as "because of something," as do other dictionaries.
Merriam-Webster's Dictionary of English Usage (MWDEU) states that on account of has been in use since 1792 and is considered casual speech. Explaining that:
"Most [usage commentators] give it at least grudging acceptance, if
only because they regard it as the lesser of two evils."
(The greater of the two evils is using on account of to mean because, which is considered nonstandard English.)
The New Oxford Dictionary for Writers and Editors suggests using on account of instead of due to. Due to and because of are both more common in books between 1800 and 2008, with because of only recently becoming more popular than due to as shown using Google Books Ngram Viewer.
In the Corpus of Contemporary American English, it can be observed that the use of on account of is more often used in fiction but significant portion of its use does exist in academic writing, for example:
Thus within the pale of Christendom, miracles become a central feature
of the process of canonization. Believers, moreover, accept doctrines
that are beyond reason not on account of miracles, but on account of
authority. —Church History, September 2006
Overall Usage for Comparison
In comparing strictly the two phrases 'on your account' and 'on account of you' we would find greater usage of 'on your account' by comparison:
Additionally, as a slight variation to compare 'on your account' and 'on account of your', it would seem as if 'on your account' still seems greater by comparison:
But, while this may make it seem like 'on account of you' was less common, it's only because it's specific to those particular prepositional phrases. However, as shown below, when using a wildcard in place of "your" in "on your account" it's clear that the more commonly used phrase was 'on account of' having more than all forms of 'on your/that/this/no/which/his/the/any/my/their account' combined and at it's highest peak accounted for nearly 0.008% of phrases found in books from 1800-2019 while the phrase 'on your account' amounted to just over 0.000048% at its highest, a difference of more than 1,666%.
As Additional Consideration
Finally, to the point of comparison between "Google's Dictionary" in contrast to the Cambridge English Dictionary, keep in mind that "Google's Dictionary" is provided by Oxford Languages, which has a slightly different approach in their corpus and collection of data to compose their dictionaries that will include slang, regional dialects, vulgar and offensive words based on empirical evidence of their usage with the goal of describing "...the way languages are and have been used by people around the world, rather than attempting to prescribe the way a language should be used."
While Cambridge English Corpus is, in an oversimplified explanation, considered to be more geared towards an approach aimed at catering to those learning to speak, read, and write English, not to suggest that it doesn't include vulgar language but you will notice that they do have a more reserved approach in their inclusion of slang because of their belief that "Slang changes quickly, and slang words and expressions can disappear from the language. For these reasons, it is generally best for learners of English to avoid using slang."
In Conclusion
In conclusion, it's noted that this question was tagged with "British-English" which is recognized as being different than American-English in many ways. While this Short Essay of sorts has been comprised mostly from references and sources of American-based English grammar, it goes without saying that it may not necessarily apply.
So, to be sure, "on account of" is acceptable English and considered to be a casual phrase while it can also be found in more formal situations, such as academic writing. Whereas "on your account" is more often used as an expression and considered an idiom that can have varied meanings, more often used among certain groups or regions of English speakers that will sometimes include a meaning that matches that of its acceptable English counter-part, "on account of" and other times when it does not, categorized as a formulaic language.
