The usages that you mention all work slightly differently. I can find no evidence for ‘have time doing something’, so my suspicion is that you cannot infer that particular usage by extension from others. Others are nevertheless interesting.
To spend time doing something
This usually carries the sense of having a finite amount of time available, and allocating some of it to this particular activity.
It can also mean taking care over a task: ‘spending time’ to make sure that something is done well, when one might simply have done a quick job. This would often be slight rephrased as ‘spending time on something’.
Your example ‘I spend too much time watching television’ is a good instance of the first of these.
To have a good time
This means something completely different. Here, ‘time’ means something like ‘experience’, accentuating the sense of a period that you spent doing something. In this usage, the period itself is not the main concern: what you are centrally talking about is the subjective experience. You can ‘have’ a good time, a boring time, a terrifying time, a confusing time, or many other kinds. The word ‘time’ ends up meaning that you can clearly distinguish this experience from what came before and after, and identify it as having had a certain character.
To have time doing something
I have never seen this construction anywhere, so it seems impossible to evaluate your speculation that ‘Have time doing something’ means ‘Spend time doing something’, although the latter is certainly a common expression.
Time to do something
This is similar to ‘spending time’, because it usually relates to the allocation of available time. It might be more common to hear someone say ‘I don’t have time [to do something]’, meaning that it would take too long, so other pressures mean that it cannot be done.
Then again, you can also say that it is time [to do something], meaning that the appropriate moment has arrived: it is time to catch the train, or to change one’s career.
To have time for [something or someone]
This is one that you have not mentioned, but it seems potentially connected. Sometimes this will mean exactly the same as having the time available to do something.
A completely different significance relates to patience or sympathy. If I say that I have time for someone, I am essentially saying that I like or respect them enough to give them my attention or support in some way, i.e. to allocate some of my finite time to them, rather than to something else. Symmetrically, to say ‘I have no time for [someone]’ is to dismiss that person as not being worth spending effort on.
I mention this to help show the range of expressions built on the idea of time as a measurable resource. I can find no evidence for your conjectural ‘have time doing something’, but many related variations certainly exist.
