We need to know EXACTLY WHICH color head you have.
Per post #5, it’s a dichroic-filtered color head, either a DGA, Dual Dichro, or Dual Dichro-S. We also learned that the problem persists with a different timer. So the problem is not caused by the timer.
The DGA and Dual Dichro use a 120-volt to 24-volt step-down transformer The standard power supply is simply a transformer. These rarely give trouble.
There is also a more complex Stabilized Power Supply (24-volts to the lamp) that incorporates a voltage stabilizer.
The Dual Dichro-S has a built-in half-wave diode-and-resistor power supply with built-in voltage stabilizer. It produces approximately 82 volts to the lamp.
Both the 24-volt Stabilized Power Supply and the 82-volt Dual Dichro-S power supply can become unstable as they age. This is most often traced to a component called an opto-isolator (trade name “Vacutrol”). There are several other electronic components in the voltage stabilizer that might have failed.
As mentioned by others, the lamp pins or the contacts in the lamp socket might have become corroded and cause the problem. The socket can be replaced. The socket is not a Beseler part and is available for a moderate price via Internet search.
One way to at least temporarily “fix” the problem of a corroded socket is to install and remove a lamp 10-12 times in succession to lightly abrade any corrosion from the pins or socket contacts. This might restore normal conductivity, at least temporarily, until you can secure and install a new socket.
In my case, my Dual Dichro Stabilized Power Supply kept burning out new lamps within a few seconds of powering the lamp. I measured pulsing voltage spikes at the lamp contacts as high as 60 volts. My solution was to replace the stabilized power supply with a standard power supply. It now works reliably, no more burned-out lamps seconds after installing.
For accurate color work with the standard power supply, you can install a voltage stabilizer between the wall outlet and the power supply.
If you have either of the two voltage-stabilized versions discussed above, there is a good chance that it is the source of the problem.