As bobequus stated, a small dip as the A/C turns on will have little to no effect. If, however, the A/C drags the power line down when it operates then you may see some effect. If the living room lights don't dim a little when the A/C kicks in then you are OK.
The common UPS units for small computers won't be any help as they are made to switch over to battery power when the power fails and not when it dips by a few volts. You can expect a 10-20V dip when the system is running on the battery. An expensive unit that runs on the battery all the time, using the power line to keep the battery charged, gets around the problem but this is massive overkill.
If the power line voltage gets dragged down by the AC, and not merely blipped, then the most cost effective solution is a ferroresonant constant voltage transformer; these are commonly made by Sola. Don't get a larger ferro than you need - ferros draw a constant current independent of the output load, so a 500W ferro with a 75W enlarger bulb will draw 500W; get a 75W ferro instead.
Plug the transformer into the timer and the enlarger into the transformer. If this sends your timer into a tizzy then you need a new timer.