Included is a picture that is exactly like my oldest Homelite. The others are all Super XL's
Not sure about the XL-12's but the oiler systems on the SXLAO's are generally pretty good.
A few issues I've come cross that makes them fail.
Oiler pick up hose in the oil tank rotted off or crac ked.
Oil lines, pick up screen, check valve (manual oiler) plugged with crap. Remove and blow out the tubes (XL-12) and on the Super XL, the passages behind the pump.
While you have the pump off, take it apart and give it a good cleaning.
On the Super XL change the "O" rings on the tube if they are worn or missing.
Check the two little "O" rings on the back of the pump for condition and presence
I think the most common I've come across are air leaks in the system. The XL 12 compression fittings are either loose or someone has cranked the fittings down hard and crushed the sealing rings.
Hope that helps