OK, I'm getting closer now, but still no cigar. As recommended by you guys, I took my wall switch circuit and a length of wire to a local computer repair shop. In about 5 minutes and lightening my wallet by $20, I now had those two wires soldered as per the picture.
Came home and drilled a small hole in the side of the button housing to exit those two wires and then hung the switch back on the wall and tested it for normal wall operation and it still worked.
So I hooked up those two wires to my new receiver and several attempts to make the receiver and bike transmitter "talk" to each other still does not work. So to validate that the two new soldered wires were in fact connected correctly, I took a bent paperclip and jumped the plastic connector that plugs into the back of the receiver and bingo........the garage door functions.
So, now I'm wondering if somehow there is something amiss with the bike GDO transmitter. Will be looking into how to determine that tomorrow. Any ideas let me know.
By the way..................Got a call back from Toronto, Canada from the (tech rep) for the receiver mfg in response to my previous call. As some of you have already figured out, the new Chamberlain electronics do NOT allow their transmitter to work.........so I ended up explaining to him about how to solder those wires and where so it would/could work. He was gonna pass the info to his team in the lab.