Hi Arthur, Your doing a great job here.
Firstly My car is a two fan jobbbie.

(a) Shorted out 30 and 87 on both relays - Fans operate on both - High and low speed.

(b) Removing temp sensor wires from engine does not make the fans operate. However by shorting the two leads they fans do operate.

(c) Sorting the Pig tails on top of the air dyer will not cause the fans to operate. The relay doesn't appear to "click" and even if it did I have checked the relay and it operates O.K. and the contacts are O.K - (external test)

Conclusion
(1) The engine temperature sensor maybe cactus. (another Assumption - the fans should come into play when the engine temp gets to around 105 degrees c)
(2) Some wiring problem in between the pigtails and the relay - if there is a direct connection.

Fotos below Just to make sure I'm looking at the right pigtails.