The wiring loom inside those old Russian Muffs is notoriously fragile. Kit Rae's interwebsite is pretty much THE authority on all things 'muff', chances are there's some wiring diagrams on there.
Something like [i]this[/i]...
[url="http://www.kitrae.net/music/Images_Secret_Music_Page/V8_Wiring_Diagram.pdf"]http://www.kitrae.ne...ing_Diagram.pdf[/url]
What you've got inside yours is an attempt to make it a 'true bypass' Muff - the originals only had a double pole, double throw (DPDT) switch, and to do true bypass with an LED you'll need a triple pole, double throw (3PDT), which is what you've got. The good news is that it's entirely fixable, although while you're inside it I'd recommend rewiring with sturdier stuff. If you're feeling up to it...