The derivative process is grammatically fine at a cursory glance. The -able suffix renders a word into an adjective, and the -ly suffix renders an adjective into an adverb, which can be used to modify adjectives or verbs. The Century Dictionary and Cyclopedia provides some additional details regarding that matter.
However, it is one step too far removed for it to make much sense in my opinion. The first thing that comes to mind when I read the word witness is not the derivative verb, but rather the original noun and if on first parse you interpret the root word Witness to be a noun, then the whole derivational process falls apart because the able suffix does not apply to nouns. Now granted, this does not pose a barrier to a word like Mannable, but that word is short and lacks the ness syllable which complicates the derivation because -ness is often used as a suffix to change words into abstract nouns. I do not think we have the word Mannably either, suggesting to me that we may not derive adverbs from the -able adjectives derived from words for sorts of people. I am not sure if that is the case, or if there is another problem here since witness is a polysemous word as a noun, but I doubt it would be readily understood. It is a bit of a headscratcher in my opinion, even though I know all of the elements that constitute its formation.
Witness has also been with us since the 14th century, so the lack of precedence for this formation is curious if it is an easily cognizable concept.
In my opinion, it would be better to either start from that is known as a verb first and foremost such as observe to make Observably, or maybe directly modify an adjective with the -ly suffix to make a word like obviously. Either of these words would fit nicely within your exemplary sentence, although which of them to use would depend upon exactly what meaning you wish to convey. Since you have dismissed blatant in a comment, I am assuming that you do not want to necessarily indicate that something should be obvious, or in other words easily known so I shall not demonstrate the applicability yet.
If you merely wish to indicate that it can be seen or in a more figurative sense, otherwise detected then observably would be the better choice. Allow me to walk you through the definitions in reverse:
Observably as defined by the Century Dictionary and Cyclopedia
In an observable, noticeable, or noteworthy manner; remarkably.
Observable as defined by Websters Revised Unabridged Dictionary:
- Capable of being observed; discernible; noticeable.
Observe as defined by An American Dictionary of the English Language by Noah Webster:
To see or behold with some attention; to notice; as, to observe a halo round the moon; I observed a singular phenomenon; we observe strangers or their dress. I saw the figure, but observed nothing peculiar in it.
To take notice or cognizance of by the intellect. We observe nice distinctions in arguments, or a peculiar delicacy of thought.
Compare this with the primary meaning of the verb Witness, also given by An American Dictionary of the English Language:
- To see or know by personal presence. I witnessed the ceremonies in New York, with which the ratification of the constitution was celebrated, in 1788.
We also have this exemplary context which is similar to your own, to demonstrate how observably can be used in practice, from Main Currents in Modern Thought by the Center for Integrated Education, volumes 28–29:
For the body is a physical, albeit a wonderfully complicated, mechanism (and hence is the subject for physical inquiry), and it observably engages in a wide variety of patterns of behavior (and hence is fair game for behavioral inquiry).
Take notice that unlike blatant or obvious, that this does not necessarily have connotations of something that should be known, or even the negative connotations of blatant.
If you undergo the process of discovery though, it is certainly a true sentiment that you are able to observe, or bear witness to (if you would rather), the heart beating or the stomach churning. Literal observation would require that you cut open the body like a surgeon to do it, but in a broader figurative sense taking notice of the auditory cues such as the heart thumping or the stomach churning can also count as observation.
The -able suffix indicates that it can be done, but not necessarily that it is being done.
Finally, transforming it into an adverb allows it to modify the verb engage. So with the knowledge of the question that I am presented with as of this moment, I suppose observably is the word that you want.