If it is not a strain, I would suggest both a test light and a multimeter. The test light is easier to use in an engine compartment, but it won’t check non-powered circuits. The multimeter allows you to measure (usually) AC and DC voltage and resistance, but can be a PITA to view while both hands are busy. Some do have a circuit test ‘beep’ feature that sounds a tone when the resistance between the probes is near zero (checking for short circuits and good connections between different points).
For checking your wires and wrangling them back where they belong, you can use the color codes (e.g. - RD/BR = Red/Brown) from the diagram that Sandstone posted and the Relay Box (top view) drawing. The wiring diagram identifies the relay terminals using a letter-number code, while the drawing uses what appears to be an industry standard numbering system. Here’s a cross-reference that I made up for the fan relays:
85 (n1)- B+ voltage (coil)
86 (n5)- Circuitry to control the relay (coil)
30 (n4) - B+ (switched circuit)
87A (n3) - Normally Closed
87 (n2) - Normally Open
It looks like the wire that’s in the center/background is one of the terminals with a jumper attached. Here’s a post with more wiring information about the Relay Box that shows Red/Light Blue jumpers between relays (the 2014 Patriot drawing):
That one shows a separate Red/Light Blue wire going to the Main Relay, but (as I mentioned above) for many years that power for the Main Relay was also jumped from another relay.
Oh - make sure you double-check the fuses if you’ve gotten any sparks on these wires.
Let us know how you make out.