Did you have the codes checked for the ABS system? There is a fault code stored in the system for the light and that will help us narrow the area of failure.
https://www.2carpros.com/articles/abs-warning-light-on-easy-repair-guide
As far as the pulling, that most likely has nothing to do with the light. That is basic hydraulics. You changed the caliper but the more common reason for the pulling is the brake hose that collapses and does not release the caliper. After you stopped in the video and then moved forward, the caliper was still applied.
I would replace the brake hose and flush the brake fluid system with new fluid.
https://www.2carpros.com/articles/how-to-bleed-or-flush-a-car-brake-system
Roy
BRAKE: FRONT BRAKE FLEXIBLE HOSE: REMOVAL
REMOVAL
HINT:
Use the same procedures for the LH side and RH side.
The procedures listed below are for the LH side.
1. REMOVE FRONT WHEEL
2. DRAIN BRAKE FLUID
NOTE: Wash off brake fluid immediately if it comes in contact with any painted surface.
3. REMOVE FRONT FLEXIBLE HOSE
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(a)Disconnect the brake tube (labeled A) from the flexible hose with SST while holding the flexible hose with a wrench.
SST: 09023-00101
Do not bend or damage the brake tube.
Do not allow any foreign matter such as dirt and dust to enter the brake tube from the connecting point.
(b)Remove the clip (labeled B).
(c)Remove the 2 bolts (labeled C, D) and then remove the flexible hose clamp (labeled E) from the knuckle.
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(d)Remove the sensor clamp and flexible hose clamp from the flexible hose bracket.
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(e)Remove the union bolt and gasket(s), and then remove the flexible hose from the disc brake cylinder.
Images (Click to make bigger)
Wednesday, August 19th, 2020 AT 4:14 AM