The boxy thing at the end of the linkage rod should be the hi/low beam switch. I remember seeing that when I was under my '93 YJ the other month. Take your voltmeter to that component and see what readings you get. If it is the switch you seek, the volts should change when you pull back on the turn signal lever for hi/low beam. You may also need to trace your headlight wires to see if there is a break in the conductor. Have you checked your fuses? Good luck to you!
Side note:
I had a somewhat similar problem in the past. Had very, very dim low beams but normal hi-beams. My problem was caused by a loose connection plug AT the headlight. Make sure that connection is good/secure and not corroded.