Kalia, from your photo it looks you're running a Powermatic 3520B. If so, I just recently investigated and fixed that annoying ticking noise coming from my headstock. I'll describe in hopes it will help you. On this lathe there is a speed pickup device in the headstock and behind the speed indicator. The rotating part of the device is on the shaft just to the left of the upper pulleys ... it's black and looks plastic. That black plastic thing houses the magnet that the speed switch "sees" every rotation of the shaft. For reasons that we Powermatic owners cannot fathom (you'll find this is a common problem described in other forums) the set screws on that speed pickup unit get loose over time and that's usually what causes that annoying tick. On my machine it started after I ran the machine in reverse for probably the first time in 10 years to do some reverse sanding. [STOP: before you do the following, unplug the lathe and wait for the inverter capacitors to discharge. With the lathe unplugged, pull the start switch and turn up the speed knob. If the lathe doesn't turn, the capacitors are discharged ... usually takes about 15 seconds or so. Then push the Stop button.] Anyway, to fix it you have to remove the allen head screws holding the speed indicator and the speed control switch assembly and pull them out a little ... enough to access the set screws on the speed pickup...did not have to remove wires but I did move them around a little. Then, you simply rotate the handwheel until you see the set screw on the black thing and tighten it with a 4mm allen wrench. I was able to get about a quarter turn on mine. Then you put the speed indicator and switch back in position, tighten the retaining screws and you're done. Worked for me. Hope it helps.
If that doesn't do it, we can talk bearings and how to adjust play on your lathe.