I'm using one with an electric timer, not an electronic one.

But I thought both were either totally off or totally on. I don't see
how they could damage the bulb. The electric one at least just has a
mechanical switch controlled by a moving wheel.

That's fine. What you want to avoid is anything where the power switching
is done electronically like with a triac. Even that would probably be ok
if you could be sure that it passed the full waveform when on but unless
you put a scope on it you may not know. Light dimmers fall into this
category...their dimming action is due to not passing the full waveform.

Some but not all photoelectric switches work this way. I have one like
that and it was notable for turning a lamp (regular incandescant) on and
off gradually--as daylight changed--it dimmed the bulb up or down. I
recently replaced it with one that was full on / full off with an internal
relay. I suppose there may be some electronic timers designed specifically
for incandescents lights that work the same way. But if the electronics
drives a relay to do the actual switching, or certainly an
electromechanical timer, will be just fine.