Large 20amp fuse keeps blowing

A short or overload. Get a wiring diagram. Find the circuit. Disconnect items on that circuit one at a time. If all are disconnected and the fuse still blows, you've got a wiring harness issue.

I am wondering if the fuse blows instantly or whether it lasts a while?

Fuse ratings for cars are usually mean or average values so a 20 amp fuse needs roughly 40 amps to cause it to instantly fail. I have not heard of a cigarette lighter needing that much current so I guess there is a fault that should be located and cured before you have a fire.
Maybe it is the element that is faulty...

I think fitting a 25 amp fuse would be slightly foolish...

what does it drive - search for some shortcut/ burnt device, wear on cable insulation through 20 amps do not blow without reason. Maybe badly connected engine mass connection - check battery connections to start with

ah , you know the fuse number, that is good.
ahhhh its not fuse 20 its just a 20amp fuse. and you failed to say
what fuse name it is or the true #
engine stalls.
and does the dash waring lamps go dead too????
if yes, that means the EFI system has no electrical power, and must stall. THE EFI needs 10 to 15vdc at all times.
im looking now, at a Real FSM ,
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

fuse #20 is horn
but id bet you told me the wrong fuse number but in the stead
the amps. which is near useless to me.
fuse 9,16,20, 21 are all 4 , 20amps.

so look at the wiring page 8w section in FSM above
and see the fuse box, and then tell me what fuse blow.
name or REAL fuse number.
and we can work from there.

you might want in this case try a higher rating fuse, example is if the fuse is 15 amp rase it to a 25 amp fuse,try not to go over 40 amp if possible,if that still blows it is more than likley a shorted switch or a bad relay causing the overload or short. after the fuse change an still a problem chech the relay for the break lights next,these are located in the engine compartment and on some models in the trunk,good luck,Gary

That circuit F-2,may be shared with the cigarette lighter and it may be causing this,disconnect lighter wire and see if fuse still blows.

U have a positive wire making ground

The 20amp ga/idle fuse powers a hot fuel module which powers the oil pressure switch, the fuel pump relay, and the fuel gauge in the tank.
Any of the four components including the fuel pump can blow the fuse.

Using a smaller fuse should make the problem happen more often.
A mechanic would unplug the pump harness at the tank and check the circuit for high resistance or a short to ground.
If nothing is found in the harness, I would suspect the pump in the tank.

make sure of two things one is any wires touching at the starter to ground or melted and or is the starter drawing too much amperage causing the fuse to blow.starter may have a dead short in it.