The 10V is of no importance at all. That kind of variation could occur in normal use as loads are turned on and off the mains supply.
Sounds like you have an internal power supply problem in the base unit. I would guess it should still give some signs of life even with the iron unplugged.
Brian.
What signs?
It has two transformers inside, one 120 to 24 and the other 120 to 12 and 24. Both measured ok. In fact as you mentioned the 10v difference seemed to play no role as I measure 11.8 and 24v which thould be ok.
It seems that this uses separate transformers for the iron and the pump. I guess so, because thease are the more power hungry parts.
One thing that worries me, there is a little 250v 200mA fuse onboard, near the transformer output, that is soldered onto the pcb and looks like an electrolytic capacitor in shape.
I cannot test this since there are no pads there.
I have to flip over the pcb, which on the top side has standard components and at the bottom side smd ones. but all smd ships are 8 pin types, I do not think there is a micro there.
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As I recall, Weller used relay to activate heater , listen for sound or check internally.
No there is no relay in that unit, I have checked it. Swithing must be done electronically somehow.
I can see a BT138 triac connected directly with it's one pin to one of the thickest cables that go to the iron connector. Switching must be done this way.