Solenoid looks like a Borg-Warner Overdrive unit. What's it out of? Found this, even has troubleshooting. http://www.fordification.com/tech/overdrive.htm
I got them from a friends widow. I have 2 of them so no idea what them came out of. I'll probably never use them but will research them. Thanks for your help.
Yes, those are the highly sought after, full synchro, Saginaw overdrive that's often used to convert a Saginaw 4 speed to one with overdrive. Usually bring a good price. Too bad you're on the other side of the country, or I am. I have two of the Muncie 319 transmissions. I had two Saginaw 3 speed with overdrives at one time, but sold them. now I can't find one locally. I am Butch/56secdandelivery.
Yep, overdrive, the lever that I circled with purple is the overdrive lever that operates with the cable from the handle under the dash.