I can't help with this specific timer but....
A while back I aquired a Kearsage timer that did the same thing, I was stumped until I opened it up.
Some previous owner had un-soldered the wire for the enlarger output and soldered it to the safelight output.
So, when turned on the enlarger and safelight were both on all the time. When I would hit the expose button both would go out.
I re-soldered the enlarger wire to the correct output and it now works as designed.
I don't know why someone would wire one this way.
Hope this helps.