Getting “tingle” from my machine.
 

503 Singer bought new in the 1960’s by my Aunt so I am 2nd owner. Good shape, sews great. When I lay my right arm on the machine bed to begin sewing, I get a mild electric “tingle”. As the machine begins to pull fabric, I automatically move/raise my arm so it’s not bothering me then. I do unplug when not in use.

a). Should this worry me ?
b). Will it be a costly fix ?

A. Absolutely.. if electricity is going where it shouldn't, it can kill you. Obviously, not yet but old wiring isn't always up to the task. I know the 503 uses an odd connection to the head, but can you borrow another power supply and check it out? plug it into a ground fault outlet if you can, next option should be a power strip with a breaker.

Others will have some ideas too.

It already worries me. Have no idea of the cost for fixing it, but the cost for not fixing it - you - is way too high.

I spotted a controller with cords for around $40.00 Still could be your lamp or something in your motor. If you are near Kansas I'd let you try a power supply. Don't try it barefoot.

be very care full
Sounds like you have a ground fault .
Could be a easy fix maybe some thing loss.
But make sure you never touch some thing else that is plugged in even if it is turned off.

The controller shouldn't cause any tingling or rogue current in the machine itself if it needs to be checked. Check insulation on the electrical wiring and plug ends, you should be able to detect were something has gone wrong. Have someone check it for you, these machines are made to a high standard and something is wrong if it happens.

I'm one of those people who is sort of scared of electricity so I would definitely have it checked out. My OSMG charges about $125 for a thorough cleaning and check up and I consider it money well spent. I'm probably going to take my new white FW to him for a general checkup just to make sure everything it working okay.

Voltage meter
 

Get a voltage meter and start touching touching the machine with both probes in different locations to track down the area at risk. Mine was with the lamp , the previous owner had used foil to tighten up the light bulb. Removed the foil and problem was solved.

A good idea about the voltage meter. make sure you have it in a 110 A.C. range and have one probe to a bare screw. Enamel doesn't conduct electricity very well.

Yeah, that "tingle" is when the electrical system of the sewing machine connects to and confuses your electrical system, including your heart. No machine is worth the risk IMO