Just so you know, there were no '51 Kaiser Manhattans. Kaiser did not adopt the 'Manhattan' moniker till 1952 when the Frazer was dropped. If the car is a '51 Kaiser and needs the relay with plug connector on it, there are vendors in the club that sell them. Also there is member in the club who reproduces the wire harness. You have to be very careful when doing the wiring in the OD circuit as some wires are 14 gauge, some 16 and some 12. It is very important that wires requiring 12 gauge wire are using 12 gauge wire.
All '51 - '55 Kaisers used the same relay and harness if that helps.
The Studebaker, Willys, Nash and Hudson (and probably some others) relays without the plug pins are the same electrically and will work fine. They just need to be connected properly with eye terminals as you point out.