Wondering when I should do it. Right now I do it at least once a month with the YYJ thin lube. Should I do it more or just stay the same?
I hardily ever lube, but once a month sounds about right.
If your yoyos are playing unresponsive and you like they way they play, don’t mess with what you’re doing. 
Once a month for an unresponsive yoyo is overkill for some of us (depends on frequency of play of that particular yoyo!), but if that’s what you seem to need, why mess with a winning formula?
If you want thinner lube for more tuning up or keeping it in good condition sewing machine oil is great. I use it on my bearings it works great!
There is no formula. some never lube. I mean ever. Some never clean their bearings. Some lube often some lube only when a problem pops up.
This is a part of yoyoing you will just figure out on your own.
I lube a bearing when it feels or sounds different.