There are multiple problems with your unit.
(1)the obvious ignition issue
(2)the fact that your cycle light remains illuminated when the thermostat knob is in the off position.
(3)Poor flame transfer on the bake burner

Have you made any attempts or has anyone 'looked' at it recently? If yes disregard any of the below and explain to me what has been done/attempted.

(1) since it's both bake and broil that previously worked, with nothing being changed (on unit or home electrical) it is probably the DSI board at fault. The board is not accepting the rectification of flame from either electrode. The DSI board is located on the rear of the unit. It's got some incoming wires and two wires outgoing to each ignitor (bake & broil). The P/N is PA020035 for the DSI board on your model #. I saw your model on a different site that would not allow me to register to respond. Please don't follow the advice obtained there by ordering the spark module...they are different and the spark module explained to you there is for surface burners only.

(2) Your cycle light should turn off with both knobs set to off...in fact it should be off any time the thermostat is turned to off. The cycle light is only there to tell you that the oven burner is on. I believe that your thermostat is also bad...either someone tried to calibrate it too far, beyond 50 degrees from set point, or the contact for the light is stuck closed. If temps are normal and you don't care about the light being on all the time, then ignore it, the light will probably burn out eventually though. If temps are off, the thermostat was probably calibrated too far out of range and you should replace it. Thermostat P/N PB010186

(3) This is less significant but an observation made on your video. The flame transfer should be more even. at the rear of the burner there is an air shutter to adjust air/fuel mixture. I'd close that a bit so that about 1/4" to 3/8" of an inch is allowing incoming air only. Depending on age (first 6 of your serial number) there was a new bake burner released for poor flame transfer. New burner P/N 006197-000

Hope this helps, and again if someone has already attempted to repair this issue, my above comments could be way off, and it could be something as simple as a wiring issue...sometimes easily caught and corrected...sometimes not.