They don't like being in backwards if polarized, or AC got to it.

That would be my guess.

LTG : )

You have your capacitor drawn upside down. Positive is the --- straight bar. Did you connect negative of the capacitor to the + of the bridge rectifier, just as you drawn it?

Anode on a capacitor? Electrolytic capacitors have positive and negative plates. Diodes have an anode and cathode.

I would avoid getting cocky if you are asking for assistance around here.

As an electronic engineer with over 40 years experience I can tell you I have NEVER heard anyone refer to a capacitor as having an anode/cathode - I don't care what Wikipedia says - they are WRONG!

You will need a cap with AT THE LOWEST, 63V rating for your application. You should also refer to the application data for your chosen regulator. They require a small cap on the input and output legs as close as practicable to the part to prevent oscillation.

Build the circuit WITHOUT the regulator attached and measure the voltage at what would be the input to the regulator. If it is higher than about 45VDC (very possible) your regulator won't like it - again, refer to the data sheet for exact voltages.

Good practice would also dictate adding a fuse in one of the AC leads at the very least.

You should also connect 0.1 uF capacitors from regulator input and output to ground, as near as possible to the regulator. The 78XX regulators have a tendency to oscillate without these caps.

BTW, maximum input voltage of the 7812 is 35V. I'm afraid that could be exceeded in your circuit.

See the post 2 above yours....

"You should also refer to the application data for your chosen regulator. They require a small cap on the input and output legs as close as practicable to the part to prevent oscillation."

Sorry. Great minds think alike

When I do 'mods' like this, I usually like to start from another power source.. For older machines like this, I would probably avoid any strain on the existing power, and just run 12v from the service outlet. In this way, you would need to power the new lamps with a relay circuit. This might give you more flexibility with the trigger input voltage depending on what sort of relays are available. Not sure if there is something lower you can work with in this case, but just an idea anyway.

There is a major difference between battery and capacitor. A battery converts chemical energy to electrical energy when discharged, and the opposite way when charged. A capacitor however stores electrical energy in electric field between its electrodes. There are no chemical reactions involved.

Your next step -- check ebay or amazon for an inexpensive regulator module.

No, not at all!

But you might just have realised that to be knowledgeable in electronics requires YEARS of tuition, study, working in the field and stuffing up many things!

You can't possibly understand the myriad of things you need to know to design even a simple circuit without the above.

Often you can learn more from non-working circuits than from those that work the first time.

28VAC through a bridge with a 25v rated capacitor. That is probably exactly your issue. Use a at least a 50v rated cap. Your 28vac probably ends up being around 40dc peak. Most cases it is recommend to use a cap rated at least 1-1/2 times to 2 times the working voltage, you can't really fudge on voltage ratings, the capacitor company would sell them as higher rated caps if they actually could handle it.

Don't be discouraged, your probably almost right there. Blowing up home made stuff is part of the learning process. Now you know to beware of capacitor bringing up the voltage to the peak after the bridge

PS your capacitor symbol is drawn backwards in your paper schematic. Make sure you get the polarity right or they will go bang.
Make sure you wired up the bridge right too.

Depending on what you want to do the recommendation of getting an off the shelf voltage regulator module is not a bad idea. They are usually built around regulators that will be much more efficient than a 7812.