the stock fan , when the low side relay is activated power is supplied through a resistor mounted at the fan and this gives you low fan speed , when the high relay is activated the fan is powered direct (no resistor )and runs in high speed
the dual fan both fans run but needs power to both power in wires to get high speed.
when you activate the low relay manually you have low speed but when you switch to high you turn off the low and activate the high relay and still only have one power wire active and get low speed operation
if the car is running and at temp that the fan would come on then activating the high speed relay the fan should run high speed mode
if you are using a caspers adapter to stock harness i dont think that adapter allows you to select high or low
if your wiring will allow low and high operation through stock relays and you are running a stock chip then turnon temp will be high (190+*) and fan will only come on in low speed when a/c is on unless temp is above 190 but if you run a/c and manually turn on the low speed relay switch than you should get high speed.
i run the racetronix hotwire
with the rtx both fan power wires are powered using stock relays to turn on two relays being fed direct from the battery ,
in normal operation i have low speed when temp is above ecm fan turn on temp (for my chip that is 168*).
turn on a/c when low speed fan is being commanded by ecm and I have high speed.
I also run a single manual switch wired to the stock high side relay which grounds the green wire ,
turn on manual switch when temp is above ecm turn on and I have high speed once it drops below temp i have low speed .
turn on manual switch when temp is below ecm turn on and i have low speed for cool down in the pits.