Hi,
Sorry if there was a misunderstanding, but the wiring diagram shown is in fact designed to show my own, modified system, using two relays, rather than one. I bought a new relay (a replica of the original Lucas unit) it would come on when required, but the terminals welded together under the current and refused to separate. I was using modern fan motors as mine were missing; maybe they drew too much current. Anyway, I designed the circuit shown too and made the rather crudely drawn PowerPoint slide to prove to myself it worked. I later sent this to David to post and clearly did not make it obvious that the design was for a twin relay system.
(David, can I suggest you modify the original post with my drawing in to show that it is in fact a modification, sorry if I did not make it clear all those years ago?)
I felt two relays were better than one so that if one failed, at least one fan would run and I also used modern relays rather than the original design, partly because I had some available, partly because of my experience with the replica relay failing.
All this, does not help solve your problem, so here are some thoughts:
First, the correct diagram:
However, you say the fans are operating on a manual switch. If so, the diagram may be inaccurate for your system, but the switch is probably in the same place as the relay, at least, as far as the circuit goes.
As Marek says, the fans operate in parallel, supplied from one relay (switch). Therefore, if one fan is working, the relay is operating, or in your case, the switch. (It is possible the switch has internal issues, dependent on the design, I can't comment further without seeing it).
So I think it likely your problem is the wiring, the connections or the motor itself. The motor could be lazy, for example the brushes on the point of wearing out, just enough to make a contact sometimes and keep the motor running, but perhaps not always to start it. Alternatively, the wiring inside the motor may be suspect. (edit, just noticed that you changed the motor, so ignore the last)
Whilst the wiring connections may be clean (as you cleaned them yourself), the wire may not in fact be making a good contact with the contact(s), due to being loose in the crimp or, more likely, corrosion in the tail of the connector(s). The wire itself may be breaking down inside its insulation. All of these can happen after 40 plus years of being located in an area which can be hot, soaked with salt water from the roads, or both at the same time, for prolonged periods. In my own case, I built my own wiring loom, hence the circuit diagram I drew to prove the system to myself.
Multi-meter tests will help, but rather than just relying on simple connection tests (usually with a "beep test"), check the resistance of the cables and connectors - often there is enough current flow for a beep test to work, but a resistance to full flow, this is usually associated with corrosion. Don't forget to test the earthing, which is often overlooked and taken for granted.
Finally, auto is better than manual when working correctly, although the original switch can be temperamental, so I suggest you get a modern sensor and the correct housing for this (Mike at Coolcat is the best source), re-install the relay (preferably a modern or well tested original one) and replace the wiring. I'm pretty sure you can buy a complete fan loom from someone like Autosparks, or you can make your own.
Hope this may help,
Regards,