Have you made any progress with the permanent taillight?
You say you have checked the connections at the taillight and that they are ok. These connections are from a sub loom, have you checked the connections at the other end, under the seat?
Not sure it’s possible to connect the black feed to the brown taillight feed as the connections should both be female but it’s worth checking (in the head light bowl).
It is worth checking the function of the ignition switch but in my (limited) experience problems with the ignition switch usually lead to things not working rather than working when they shouldn’t.
The taillight works separate from the head lights and is powered with the pilot light (small separate bulb) in the head light bowl. Is the pilot light on when the taillight is on?
Is the pilot light bulb ok?
Does the taillight go off if you disconnect the front or rear brake light switch?
Are the speedo and tacho lights working ok?
An easier mistake for someone to make would be to cross connect the brown and brown/white connectors in the head light bowl.
Lot of questions but as Bryan says it’s not easy to diagnose electrical issues at a distance.
Not sure what work was done on the bike and whether there was any reason for anyone to disconnect any wiring unrelated to your engine refurb.
