The wiring would appear to be fine, depending on what you mean by 'bypass' the switch, I guess you mean bridge the connector?

The standard switch (red) closes at 86°C which is to early, in addition it keeps them on for too long.

For this reason a "uprated" switch is available (merely closes later and runs the fans for a shorter cycle)

As your new to them, the fuel pump wiring can build resistance, thus the pump cannot draw the current it needs under load, which can lead to a meltdown!

The solution is to rewire the pump, both of these are common problems.

They are automated for a reason, so no, don't be temped to add a switch.

Martin