Apparently I don't remember things well, as he used air, not an electrical solenoid. Here is what my dad sent me in the email.
After melting 3 cables, getting the locker to work only once each cable, I followed your recommendation to replace the cable with an air cylinder, as described in an article you told me about on the internet. The cylinder is a Bimba, and as I recall the bore is 1.0625. That is the largest that has the correct shaft threads. I used 1/8" nylon tubing and fittings. The biggest problem is that it takes about 100 PSI to operate it consistently. I modified the plumbing using a 4 way 5 port valve backwards, so I could use engine vacuum on the other side of the piston when energized so only 85 PSI is needed. I added a small air tank and a small air compressor and pressure switch, independent of my removable 12V compressor for airing up tires. I still don't need my locker very often because I have limited slip in the rear and excellent articulation, but it is very nice to have when needed. I hope this helps.
I looked on the ox website and they seem to be selling an air actuator and an electrical unit as well to replace the cable so if you have more money than time and aren't adventurous to trial and error you already have a possible solution without buying a new locker ~$150 on their site.