Never under-estimate a mouse and the damage it can cause.
A bad ground or hot wire connections is also possible. There's also been several discussions on here about the voltage drop in the overhead lites - the wire-gage isn't large enough to handle the current draw of the lites.
When the bulbs were new, mine would almost always fire-off right away, but as they aged they got slower and slower and at times would flicker or not even come on (hmmm... kinda like me
). After several rounds of replacing bulbs, I got fed-up and replaced everything with LED strips. Brighter, more-reliable and less current draw.
Probably not the answer you were hoping-for.