Should it run when the AC is switched on?

The car was cold and I turned on the AC at idle to see how the AC felt (its getting a checkup soon) and a friend suggested I check the fan as well since its weak around town but okay on the highway. AC felt cool at idle but the auxiliary fan didn't kick on.

I put 12V to the connector and the fan does work.

So if the fan is supposed to kick on when the AC compressor comes on, where should I look now? Relay? If so, where is that guy.

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