yup, from the looks of it you have a Toyota 4P-PNE5 engine
It is a 1493cc OHV engine

Now from what you described of the things you have already done to help eliminate what the noise "could be" I'm assuming by taking off the belt you eliminated the alternator and also the water pump? And still had this clicking noise coming from the "front" of the engine? (radiator side of engine)??
If this is the case you want to check some things.....

1) check the distributor in the cap area, even pull it out of the block and check the gear, look for any signs of anything broken or worn.
2) check the valves, yes pull the valve cover and check the valve clearances and make sure all is well there, no broken springs or loose valve adjustments.
3) check the fan drive, if part of the water pump?, then double check the bearing on the pump.

from the looks of the illustrations i can make out in the manual there are gears inside the front cover, if you donot find anything from what i mentioned above then you can pull the cover and inspect the gears and make sure none of them are out of order, damaged or chipped teeth , anything as such.

Generally a clicking noise can be associated with valves out of adjustment or maybe even spark plug wires breaking down and arcing against the head somewhere, even inside the sparkplug area. (This is another thought to check on)
I would do the easy things first, then go from there. :o)


Some points of interest that may come in handy
Valve clearance:
Intake:0.20
Exhaust:0.36

Points Gap:
0.4 - 0.5mm
Spark Plug Gap:
0.7 - 0.8mm
Cam Closing Angle (I'm assuming this is Dwell)
50 - 54deg

They do not list a single timing degree , they show timings for intake and exhaust valves on opening and closing and also talk about an octane degree setting. I wont go into that at this point because its more info that will just confuse you for the moment. Just try the things i mentioned and then we can go from there.