I suspect that the control function for one or both of these fans is actually both timer and relay...
probably both in the same component that are commonly called "fan relay" or two separate fan relays.
IF this was my DIY trouble-shoot/repair project, I would try to:
(a) determine the actual current loads there are when:
...... (1) the one fan is operating, and
...... (2) both fans are operating
(b) and then see if I could find out what the "continuous operating amperage"
rating is for the OE relay/relay(s) are.
IF these relays are not rated substantially higher than the actual amperage loads,
then this could mean the relay's power-on contacts stick closed and
then subsequently release due to cooling off or vibration!
--------------- Try this ---------
IF it stays on again... after you turn off the key and it has cooled some,
"rap" on the relay's outer case and IF the relay turns off in response,
well this is strong evidence as to what is happening!
You can purchase heavy-duty 50A, 100A & 200A industrial relays
for far less than what I suspect VW OE relays cost!
I did this to solve my repeated Glow Plug burn outs on my Mercedes 240D!
My last two 100A relays cost me less than $20/ea...
and I will be adding one of these to control
my new '81 VW Caddy P/U project car's GP system!
[IMPORTANT edit] - Keep in mind that these electrically controlled fans are
IMPORTANT in that they help to solve overheating and
damage to the aluminum heads that "percolate" when the engine is first shut down...
and the fan's continued operation is needed to reduce the
potential for warping or other damage to the weaker parts of these heads!
So don't let your zest to come up with a DIYer solution for "run-on" fans
end up costing you major engine damage!
Regards,
Sam Ross