in my case the start winding (w3) was approximate 2x ohm value of the W1 or W2 ( run windings)
when all wires are separated out, you should have 3 set (6 wires) of wires (maybe 4 sets (8 wires) if you do have tcs) make sure you kept the 1 2 3 4 marked it is important.... otherwise if you get it lost the magnetic field generated might cause problems to the spinning rotors, if you get those reversed....
as far as the wires gets lost, it's probably inside those yellow tubes that is either fiber glass or silicone (they are a bit tougher than heat shrink.) Your TCS is probably inside there too.. The strings that tie them together is just regular cotton string I think... Mine was inside those tubes, I have to cut the cotton strings and free them carefully... Keep in mind before you start this is almost the point of no returns.... so...
safety first yea even thought it's 120V it's consider high voltage that can kill you... sorry bud. probably not a great thing to advise in a forum.. and probably a lot of experts hesitate in answer you these kind of questions.
when I was modding mine and void warranties, I think I remember some of the supplies needed are.
make sure you have some cotton strings
some good size plastic ties
some silicone / fiber glass tubing, just few short pieces of 1" or 2"
few pieces of 14 gauge stranded preferably machine tool wires...
MTW wires
and crimp connectors to crimp the wires back together. They are mechanically tied together as oppose to soldered. I used the end of a small 18 or 22 gauge or so crimps and snipped off the ends I don't need.
****I don't know what that ?2 marked wire is in your pic. That might be one end of your start winding... was it connected to something like 4? or 1?