Odd brake/tail light problem

The brake light switch should have power at all times regardless of key on or off. So from there it is a simple matter of chasing the circuit back to the fuse panel

In the meantime in order to check that brake lights power is getting through the TS switch, you can jumper 12V into the brake switch wire that feeds to the TS switch, I believe it is the white

Make sure the bulbs and the pigtail contacts are indexed properly in the sockets. When sockets get rusty, or pigtail insulators become damaged, they can twist in there and not make proper contact.

I assume you know how 1034/ 1157 bulbs work. The shell is common, one contact is tail, the other brake.

I don't know why two (new?) bulbs would be blown, unless poor quality, or maybe the charging system is over voltage?