If I understand correcty, 2 batteries doing the same thing, clicking, headlights slightly blink but stay bright while starting the bike.
By now I hope you have cleaned both ends of the positive and negative cables, and made sure that all 4 connections are tight.
Inside the solinoid of the gear reduction starter are 2 contacts and a disc on the plunger. When the 2 contacts wear out it makes a poor connection, leaving you with this clicking symptom.
You can remove the 3 small bolts that hold the cover on to look at the contacts. New are about 1/16 of an inch thick, where they contact the disc on the plunger.
By now with the age of the bike they could be worn down. You will need to remove the starter to replace them, keep the nose of the starter down and the cover of the solinoid up, and off, there is a small ball bearing at the tip of the plunger shaft. Remove the nuts on the side of the solinoid and push the stud in for removal,
There are insulators that need to be on these studs so remember what comes off when comming apart.
After these contacts are out you can pull the plunger out. Take these parts to NAPA or if there is a alternator / starter rebuilder shop close by go there for them.
These srarters are very reliable, the contacts are almost always the problem and are simular to Chrysler starters and we replace the contacts and plunger kits alot. Much cheaper than a new starter