Termite damage on stub of cut limb... seal?

Hi guys,

Newbie here... I've googled this and haven't come up with anything.

I have a situation with an avocado tree where I noticed some termite damage on a large limb that I deemed hazardous. I cut the limb off in pieces, eventually back to a stub off the main trunk, piece by piece looking for where the tunnels stopped. At the stub, going into the main trunk there are still tunnels. With all of this said, I didn't see any active termites in any of the wood cut... just some small black ants. I treated the exposed cut and tunnels with imidacloprid and at this point the cut and visible tunnels going into the stub are exposed. When I poured the insecticide into the tunnels, it appears that most of it dripped from the bottom portion of the tunnels exposed in the cut... (Potentially indicating those tunnels might not continue far into the rest of the main tree trunk)

My question is, should I inject something, (e.g., caulk, silicone, tar, epoxy resin?, etc) into the tunnels to seal them and prevent any further intrusion... water damage, etc?

I understand the generally accepted practice is to let a cut heal itself without being painted, but I've found nothing on this when there are exposed termite tunnels in the cut limb stub...

The rest of the tree appears otherwise healthy...

You're out of my area of experience but I will pose a question. Are you sure this is termite damage and not ant damage? I know of several big old hard maples that have been taken out because of ant colonies.