How do you repair a 4wal anti lock system that causes a weak pedal after start with a strong pedal before starting.

You do not bleed brakes in an "X" pattern. You start bleeding at the wheel furthest from the master cylinder. Once that wheel is bled, move to the next furthest away from the master cylinder and so forth. Doing it in and "X" pattern would leave air in the lines.

possibly a faulty caliper

Sounds like it might be your master cylinder that is bad.The seal around the piston inside the master cylinder is allowing fluid past it therefor letting the pedal go to the floor.

Good question, on the antilock system is a bleader too and bleade it the same way you bleade the caliper. After all is done adjust the rear brakes, they should have a drag to them.

Check Brake fluid level.

When the ABS light is on, the brakes should revert to standard braking.

The only time ABS should invoke is when the tires are slipping as sensed by the wheel speed sensors when the wheel locks up on any of the axles.
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ANTI-LOCK BRAKE SYSTEMS General Information Fig. 1: RWAL brake system diagram
Fig. 2:4WAL Component locations — except 1996 models
p>Fig. 3: 4WAL Component locations — 1996 models Fig. 4: Three sensor 4WAL brake system diagram — Except 1996 models
Fig. 5: Four sensor 4WAL brake system diagram — Except 1996 models
There are two basic types of anti-lock systems available for this vehicle; a Rear Wheel Anti-Lock (RWAL) brake system and 4 Wheel Anti-Lock (4WAL) brake system. The 4WAL system has two variations; a 3 sensor system and a 4 sensor system. The 2WD vehicles will be equipped with the 3 sensor system, but the AWD vehicles can be equipped with either. The systems are easily identified by looking at the rear wheels for a sensor harness. If there is a sensor harness and thus, rear wheel sensors, it is the 4 sensor system. If the vehicle is not equipped with a harness, it is the 3 sensor system. The 4 sensor system takes it speed references from each of the wheels. The 3 sensor system takes its speed references from each of the front wheels and the vehicle speed sensor located in the transmission (2WD) or the transfer case (AWD). The RWAL system components consist of the Vehicle Speed Sensor (VSS), the Electronic Control Unit (ECU), the isolation/dump valve and the Vehicle Speed Sensor Buffer (also known as the Digital Ratio Adapter). The ECU also receives signals from various brake switches. The 4WAL system components consist of the Electro-Hydraulic Control Unit (ECHU) valve (also known as the Brake Pressure Modulator Valve or BPMV), the wheel speed sensors, Vehicle Speed Sensor (VSS) on 3 sensor systems and the VSS Buffer.

That is the abs unit, be nice to it

your power brake booster is blown out
the seal has a leak in it
run the truck for 3 minutes and shut it off. with the windows up listen carefully while you gently apply the brakes
listen for a hissing sound of air leaking.
the sound of these leaking is a very soft sound

make sure you are bleeding them by doing them as an abs system,do the right rear then the left front,then the left rear then the right front,the opposite wheels are how the system brakes.

adjust your rear shoes up so that the rear drums just turn, with them ajusted to a low setting the brake pedal will be low .
also when you start your engine it is noral for the pedal to drop because of the boster ! [ but not to the floor ]
Bruce Pike

depending on the system if it is 2 channel or 4 channel one of the sensors that are located on the backing plate located behind calipers is eithier faulty or dirty you can try brake cleaner these sensors use a small magnet pickup device to sense when the wheel "locks up"