I thought I had diagrams for this stuff, but I can't find them. My oil cooler fan will spin when the starter is working AND if the fan thermostat switch calls for cooling, but it has never been an issue. From my car manual:
"The Oil Cooler Fan: Located in the driver’s side rear wheel well, it is managed by a 180° thermostatic switch in the oil line on the input side (top) of the cooler. The switch drives a relay inside of the engine compartment just ahead of the ignition coil on the driver’s side inner fender wall. Power to the fan is fed through the relay from the battery and energized by the thermostat and the ignition circuit such that, even if the fan is operating, when the key is turned off the fan will stop."
So, without a diagram, power goes from the ignition circuit ("+" side of the coil) to the thermostat switch, then the other side of the thermostat goes to the relay coil "+" side, and connect the relay "-" side to ground.
On the fan, the "-" side to ground and the "+" side to the normally open side of the relay, and the arm of the relay to a fused link to connect to the solenoid/battery post at the starter.
All I have on the oil circuit is this, so far:

Here's the section out of Pearl's service manual:
2.5.2 Internal Oil Cooler
It uses the larger, 1972, stock VW internal oil cooler within the fan shroud. The shroud must be removed to service the internal oil cooler. It has two O-rings between the cooler and the engine case and an extra cooler shroud on the back.
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2.5.3 External Oil Cooler
In addition to the internal oil cooler, the engine case has been modified for “Full Oil Flow” directly from the oil pump out of the pump cover to an external oil filter and cooler. The external cooler is a 16-pass, fan assisted, DeRale cooler mounted in the Driver’s side rear wheel well and plumbed into the oil delivery system with ½” ID hoses with AN-8 fittings. The cooler fan is driven by an electrical thermostat set at 180° which drives a relay mounted on the driver’s inner fender wall, just forward of the ignition coil, to operate the fan. The relay then turns the fan on and off as needed. There is no over-ride switch.
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2.5.4 Oil Cooler Flow Thermostat.
The oil flow to the external oil cooler is not needed when the engine temperature is below 180°, so the flow is managed by a mechanical flow, sandwich-plate thermostat located between the spin-on oil filter and the filter mounting bracket. The thermostat used was a MOCALThermostatic Sandwich Adapter from Aircooled.net, model MOC-SP1T and is installed as shown:
2.5.4 External Oil Filter
The oil filter is found next to the Driver’s side engine valve cover with a mounting bracket attached to the car frame.
The filter is a Napa Gold 1515 (a WIX 51515)
The engine oil pump has a pressure relief valve (set at 125 psi.) which is part of the oil pump cover (see more under 2.7 Engine Oil Pump).
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2.5.5 Oil Flow Description
Oil flows from the oil pump to the external filter, through the filter and into the thermostatic sandwich plate.
If the oil temperature is below180° F, the oil flows directly back into the engine to the bearing oil gallery via the port just above the oil pump.
If the oil temperature is above 180° F, the sandwich plate re-directs the flow from the filter output to the external cooler, then back to the sandwich plate, from there back into the engine oil gallery.