Both brake & ABS lights com on intermitently

VSS - Vehicle Speed Sensor
Located on transmission extension, Either the VSS is bad or connector.
White and purple wires are wrapped in grounded shield ( there is even a ground wire in the wrap, for static control, since VSS is a micro power pulse generator transmitting signal to ABS which in turn checks it against the wheel sensors data).
VSS is just under $30 at dealer, but the connector with 2 pigtail wires are just bellow $60. Go figure. Oil and dirt in connector will cause the problem you specified, but GM had placed a rubber gasket around the connector which goes into the VSS terminal both for dirt and oil protection and securing the connection.
A single 8 mm screw is securing VSS bracket to transmission extension housing. Once the screw is removed just pull the VSS out, without twisting.
Heavy deposit on VSS will indicate that transmission needs some serious service soon. Clean it first with rug and clean transmission fluid, Install it in place, if it works - great! If if doesn't then New vss or connector.
Note: do not drive much with ABS/ Break lights on. Your Speedometer may stop registering the speed and Service engine soon Light may come on.
I had that experience. My VSS was good, but wire was broken at the terminal. I went to self service junk yard and got me a VSS and connector for total of $5.00. Spliced wires to connector and all symptoms went away immediately.