Programming a clicker from your Homelink?

I’m very familiar with setting up Homelink buttons for various gates, garages etc.

Is there any possible way to do the reverse? For example, I have my neighbor gate programmed to my car, but would like to program a universal clicker. Is this possible? Are certain brands easier than others? If this is possible, can I use that clicker to program another homelink? I’ve ordered an actual clicker from the HOA but apparently it’s delayed. Just curious.

Way too many variables on how it works.
Garage openers are so varied that it’s hard to get one that fits all.

Also some openers are tracked, so if you dup your neighbor’s he looks like he’s going in twice as often.

Maybe try one from Amazon and see if works out?