The 5amp fuse is only powering the indicators for all of these things in the dash cluster itself. The actual lights are on another circuit. It does not blow right away. In fact when I replace the fuse it usually lasts ~20 minutes. I did try putting a 10amp fuse in when I ran out of 5's and it also popped after ~20 minutes
Interesting.
Gotta say first, I know you know better than to do that. Putting a 10A in place of a 5A in old junk is how you melt down your cool Stout. ;-)
But since you've done it and lived to tell the tale it indicates a few things.
If you can post the exact numbers on the fuses it could be determined exactly but you can pretty roughly assume an AGC fast blow will hold 1x rating (e.g. a 5A at 5 amps) for at least 4 hours, 1.35x rating for 3600 seconds and 2x rating for 120 seconds. Beyond that the time to open decreases exponentially, so at 3x it's only hundreds to tens of milliseconds to blow.
So unless you're really far off on fuse-to-load you can usually get past initial inrush. A filament bulb can experience as much as 5 to 10 times nominal inrush, so a 2A bulb might draw 15 amps when it's first turned on but settles to 2 amps quick enough that it won't blow a 2A fuse since it's also following a warming-cooling curve. It gets trickier with non-resistive loads. That would be inductive things like motors and coils. Or when you stagger loads. So the first couple of loads don't do it but a 3rd or 4th inrush after a few minutes of heating up the fuse that does it.
Since both the 5A and 10A last 20 minutes then you can probably assume it's something large that's coming on at that point. If it was just constant load then if the 5A blows at 20 minutes the 10A will likely last indefinitely since the load is probably just a bit more than 5 amps.
But if a similar use allows both to last 20 minutes then the load has to be sufficient to blow both fast. What I mean is if it opens the 10 amp at 20 minutes then the load would be only *very slight* higher than 10 amps. But that sort of constant load would still open the 5A in just a couple of minutes.
Since both values last 20 minutes the load from zero must be about 5 amps and jumps to I'd guess 20 amps or more for some reason.
Are you sure you can't correlate it to maybe hitting a blinker. It could be as weird as your normal routine is to let the truck warm up for 15 minutes before leaving and it takes 5 minutes before you first run into a stop sign and hit your brakes, thus the first time brake lights come on or something like that.
And don't discount Jeff's idea but think dynamically, too. For example a short might only occur when you jostle the wiring driving over railroad tracks or when you turn left or right pulling only when the cab or frame experiences movement. If it's in the steering column it could be twisting a harness.
So the 20 minutes in your perspective might not actually be 20 minutes of electrical load. The fault is I think very short duration and thus easier to mimic in the garage.