How reduce battery current to zero when external power connected

[onlooker]

I guess your Q1 had drain and source connected  backward. Should IRLML6401 be a negative drain device?  Though, I can see by a strange way Q1 as is will still work: when no 3.3V supply, the source of Q1 is initially pulled up through the diode in it and that give the needed negative Vgs. Also, a small cap between VBACKUP and GND may ease the supply transition and help to turn on Q1.

As l mentioned you might even replace Q1 with a schottky, or otherwise R1=1k  is way too small. It drians the 3.3V supply unnecessarily. Make it 1M should be fine.

Q2 is acting not more than the diode in it. And worse yet, the diode has 1.2V drop(max). A schottky is better. Did you measure the voltages drops over Q2, or did I miss something?

Edited:

[onlooker]

Ok I found this quote to explain the working of Q1,

Most of the time this diode would prevent the MOSFET being useful when flipped around. There are some applications you can consider "advanced" where this diode is actually used deliberately. One example is to make a synchronous rectifier. That's basically a diode with a transistor across it. The transistor is turned on when it is known the diode should be conducting. This lowers the voltage drop across the diode and is sometimes used in switching power supplies to get a little more efficiency.

Switching drain and source should work too. But it looks like either way may have potential problems depends on other factors. With Q1 as is, there is the need to make sure to prevent both sources to compete to supply VBACKUP (Q1 through the body diode); while with Q1 flipped, one run the risk of the 3.3V supply charging the backup battery when the backup battery is low, unless  some rechargeable battery scheme can be considered.

[NiHaoMike]

I may change my mind... or change GPS module.  It is far from ideal that the GPS module also requires the battery to maintain device settings!

Could you consider using a small microcontroller to reinitialize the GPS on every boot?