In the older filament bulb signal heads, the bulbs are carefully made to place the filament at the same place, so that lampholders can be aligned in the factory and sealed into a set position, eliminating the need for on-site adjustments of the individual beams in a signal head. The heads also incorporate cast-in sighting holes to allow alignment of the whole head on site.
So there should be no need for a head to be moved once erected other than for very minor adjustments, which are built into the head and its mounting foot. Only if the whole head is being replaced will it need removal - that would require a possession and the OHLE would, of course, be turned off.
Bulbs were replaced at regular intervals to minimise the potential for failure, even though the bulbs were usually made with two filaments, main and standby. The bulbs would be changed by the S&T people using the protected access on the signal gantry and accessing the head through the doors on the rear of the signal. I believe the lens fronts would be given a clean at the same time. The OHLE would remain on and trains run normally during such work.
Modern LED heads are also set up in the factory as part of their manufacture, and again, once on site, should need no adjustment once the initial set-up has been done. There are no bulbs to replace regularly either. Some LED signals are now mounted on folding posts so they can be cleaned and otherwise maintained at ground level, eliminating the need for ladders, protective cages and possibly gantries.