High RPM = fuel pump runs at high speed.
RPM drops = fuel pump runs at low speed.
When hot and driving for hours the fuel pump resistor gets hotter and hotter. As resistor gets hotter, fuel pump voltage reduces. Eventually fuel pump voltage is too low and performance suffers or the engine stalls.
Solution: bypass fuel pump resistor so the fuel pump runs at battery voltage all the time.
That's one solution.

But is it a good one, for what this threads is about?
Jimmy, I respect the creative work you do. From retrofit with electric motor!. Modified fuel systems, to run on pure ethanol. Heat shielding, to prevent fuel boiling and vapor lock. Supper charged VVT. Even this fuel resistor bypass you've done. You're a creative pioneer!
For those that don't have time to read this long post. Here's the last few words, from Bing Chat A.I: "
If the fuel pump speed is too high, it will deliver more fuel than the engine needs, and the
excess fuel will be sent back to the tank through the return line.
This creates unnecessary heat , "

Heat!
This thread is about why fuel tank building excessive pressure "Fuel boiling" as it known.
Some say: "All land cruiser boil fuel" This simply is not true, IMHO! It's the things owners, drives, builders and mechanics do and or don't do. That increases likelihood of fuel boiling.
I agree fuel resistor gets hot. Which Toyota place heat sink fins on it, for that reason.
I've been monitoring the resistors temperature, of various 03-07 100 series. Seeing 135F-198F.
Running fuel pump with full 12V current at all times, may overcome some of the effects of resistance on wiring & pump. We've heat/resistance from end to end, even when FP resistor is not bypassed and working as it should. Keeping current/volts at max, by bypass FP resistor. Can over come low fuel flow at low RPM, by keeping fuel flow at max pump can produce. Sound good! But is resistor the root cause of lean condition stall, perhaps. But why then, does replacing fuel, solve the low RPM lean stall.
But is this just issue at resistor creating to much resistance:
If so, replacing fuel pump only, would not cure. Certainly not in the long run. But it does cure, and cures for long term! I've document in just one 06 alone, over 120K miles since fuel pump alone replaced, and not one stall. Cumulative mileage in the dozen or so 06-07 I've replaced fuel pump on, is more than 300K miles. Not one had resistor replaced, just fuel pump. Non have fuel pump low flow stall issues since. I've replaced a lot of Fuel pumps, in all years. Not one resistor or bypass of resistor in any of them. Not one issue of leaning running stall, afterwards. One creative young man. Placed his FP resistor in the air box, to cool. Which he reported, did cool it somewhat. But did not help his fuel issues (fuel boiling or stalls).
In my first (Snowy) that I learned of how to spot the symptom:
It was by studying its service History. Where customer (PO) keep complaining of vapor-lock (service manager was writing up as vapor lock), driving up to Eisenhower tunnel. It took that Toyota Dealership (Stevenson West), ~6 times into shop over first 100k miles period. Before they cured, by just replacing fuel pump. It's now has 120K more miles since replacement of fuel pump alone, without a stall.
The second was my 07 (GrayGal), I'd just purchased while driving back to Denver June 29th 2019. It stalled 3 time (Vail pass, Eisenhower tunnel and near Idaho springs). I was plugged into tech steam and logging data on my phone during the drive. As soon as stall happened, I read codes, before turning IG key off. I'd get BK1 & BK2 lean. I replaced it's fuel pump, then took on same HWY drive on a day with even higher OAT in mid July. No issue than or to this day, with stall or lean condition.
I've monitor fuel pump resistor temperatures, with IR gun:
I monitor fuel pump resistor, with IR gun for a few years. In the 03-07. Which 03-05 have different P/N than 06-07, for resistor and fuel pumps. I also recorded OAT, IAT, ECT, IR temp at fender near resistor, IR temp thermostat housing. I also note weather (sunny, cloudy, wet, etc.) and driving condition (i.e. stop & go, HWY, mtn passes, etc.) All FP resistors get hot. I see temp on days, where OAT above 90F, from 183f to 198F. The highest reading, was ones pushed the hardest on the hottest days, to test. One being the same one, stalled do to lean condition, that I replaced FP on. Still running strong today. But even on others, like my 03 w/315K. I get temps ~198F. Which it still has factory fuel pump and FP resistor, without issue.
? Why did Toyota even install a resistor or variable speed fuel pump. Bing Chat A.I. states:
Toyota uses a
variable speed fuel pump in the Land Cruiser to improve fuel efficiency and performance. A variable speed fuel pump can adjust the fuel pressure and flow according to the engine’s needs, reducing fuel consumption and emissions.
A variable speed fuel pump also helps to prevent vapor lock, which is a condition where the fuel vaporizes in the fuel line due to high temperatures, causing the engine to stall or run poorly
? Since fuel pressure if controlled by fuel pressure regulator. How does slowing fuel pump speed increase fuel efficiency Bing Chat A.I. states:
Slowing down the fuel pump speed can increase fuel efficiency by reducing the amount of fuel that is wasted or returned to the tank. The fuel pressure regulator maintains a constant pressure in the fuel rail, regardless of the fuel pump speed.
If the fuel pump speed is too high, it will deliver more fuel than the engine needs, and the
excess fuel will be sent back to the tank through the return line.
This creates unnecessary heat