Its definately your ABS Module...
the easiest way to find out if it has a faulty ABS module is
start the car & when the lights come on, is the oil light on?
if so unplug the big connector on the ABS & see if the oil light goes off.
if it does it will need a new ABS module, now there have been a few people say to remove the connector & clean it will fix it, i have never seen this as a long term repair, the fault is a known electronic issue in the module & no amount of cleaning the connector will fix it permanently.....
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