It briefly lights up for a split second, then goes away .
sometimes just the abs light, sometimes, just the battery, sometimes both.

Not sure what this means, It tends to happen when I accellerate from a stop, or make a sudden throttle increase. The ECU is not showing any error codes. Could it be something with the alternator? I had it rebuilt just over a year ago.

 

I'd check the alternator belt condition and tension 1st. The belt may be slipping.
I don't think this would affect the ABS light, but you may have separate issues.

 

it's the alternator / belt