I have found the smaller alligator clips are the most useful. The spade connectors, maybe not, because you'll only use them to troubleshoot circuits inside a connector (the plastic parts that clip together), to verify that the wire hasn't separated from the terminals (rare, but it does happen, especially if someone separated them by pulling on the wires and not the connector housings). For those, it's most useful to have the same terminals as are in the connectors themselves. The connectors and terminals are mostly Sumitomo, and
Ballenger Motorsports carries, or can get, most of them.
Having said that, I usually just use the
probes from the DMM. It's not the best setup, and sometimes it feels like you need three hands, but it works.
The two horns are separate elements, they can be tested separately. If I remember correctly (I don't have one in front of me), the wiring to the horn has a positive and ground; if so, you need to have both in the connector. It's below freezing here, so I'm not going outside to check.
FWIW, those horns are listed for Camry, Supra and LandCruiser, from 1986 to 1997.