Best Of

I'll add, don't trust what you find in the field. I've seen green wire used for power. Assume it's live, and test. 🤓

Yours, Larry

The buzzing if excessive could be a mechanical defect with the "CR" relay. You may want to verify where the buzzing is coming from and when, it may be a clue.

It is starting to look like the relay "CR" in the boiler has an issue (could be stuck, contacts welded, coil energized, or other mechanical defect). Power down the boiler, remove the Red push on connector (Yellow arrow), restore power to the boiler and see if it still fires. This just eliminates all the wiring that goes to the SR501.

As @109A_5 indicated, you have a series 1 boiler with standing pilot so this is your wiring diagram

I wouldn't be surprised if that is not posted on your boiler somewhere. I have a red circle on this diagram where the thermostat is supposed to be connected on the diagram. Here is that connection on your boiler.

In your case that is not the thermostat wire. Possibly because there were 2 zones at one time and each zone had a switching relay to operate each separate circulator. Since you no longer have two zones that control is not needed. The fact that it is still there means that you have more than one place to look for your problem. That thermostat wire has 5 or 6 conductors. Only the red and the white are used and they connect to the switching relay where @109A_5 indicated in this picture.

1. The place to start looking for the problem is in the TACO SR501 switching relay.
2. With the power off to the boiler and the boiler cold, remove both the red and the white wire from the SR501 in the red circle.
3. Power up the boiler. The burner should not operate.
   1. If the burner operates then the problem is not in the SR501.
   2. If the burner stays off, then the problem is in the SR 501.

Based on your findings, we can take the proper steps to solve the problem.

Looks like your boiler is the Williamson GWA series 1 and it should not behave as it does (similar to a warm start configuration). The boiler and the circulator should follow the thermostats command.

Looks like the Taco SR501 is wired correctly.

To start to determine troubleshooting direction start where @mattmia2 stated.

As @EBEBRATT-Ed stated the relay inside the boiler "CR" (Red Arrow) could be stuck, contacts welded, coil energized, or other mechanical defect. Note on your unit the connection plate on the transformer is spun 180 degrees compared to this image.