NJC, welcome aboard! As you have already read, I seem to be a land shark on this subject. I didn't mean to but mearly just fell into it. What you asked about backward bypassing the system would be great if you could find a way. The biggest problem would be that to do it I'd bet just about any amount of money you'd need to reflash the BCM somehow to get it to ignore the Passlock system. Also, if you could do it, my guess is that GM dealers would let that be an option outside of warranty.
For the time being, my method seems to be the best way to go. BTW, you will get a major bill from your remote starter installer. If that light is on when you go to get it installed, they'll have a real good time with your truck unless they are aware what I say on here. The reason is the exact thing you stated...."these bypasses read the resistance everytime you start the vehicle". Well, if the resistance is off like enough to get your security light to come on the bypass is worthless.
On the '98 s-10 series the BCM is down below the center part of the dash behind the black cover. The plugs face the gas pedal. Over time someone could get that a little wet from slush and snow causing the leads to corrode. I'd take the cover off and unhook the plugs and check for problems there. Then reconnect them and see what happens.
Since you now have that light on, that means the BCM is in "fail enable mode" You can read about this in your owner's manual. It means that you need to get it fixed fast. The system is so bad now that the BCM is ignoring it but it'll only do that for so long.