The best way to find cooling system leaks is with a pressure tester. The pro all use one made by STANT and sold by many names (incl Snap On), about $80.
Home Made pressure tester
The parts needed are as follows and should not cost over $20. Good scrounging will lower that substantially.
(1) small 30 PSI pressure gage with 1/8 male pipe inlet. (1) brass 1 1/2" long 1/8 pipe nipple. (1) brass 45 degree 1/8 pipe fitting. (1) brass 1/8 pipe nut. (1) tire valve stem (used is OK). (1) 16 PSI pressure cap.
The following tools are needed.
Drill and drill index up to .400" or 10 MM. Taper reamer. Super Glue. Teflon tape. Soldering iron or torch and solder. Tool for removing tire valve core. Vise for holding work while drilling. Saves your fingers!
A lath, drill press, drill press vise, all have some use but are not necessary.
The first step is to disassemble the cap into it's component parts by drilling out the rivet that hold it assembled. This is the single hardest part. Set the cap, neck washer, neck spring, pressure spring, pressure seal washer, backup washers, and spring seats aside and start drilling. The cap must be drilled and reamed to clear the pipe nipple. This will replace the rivet in the cap assembly and must screw into the pressure seal backup washer and stick through the seal washer and have the pipe nut screwed onto it to retain the seal washer. The vacuum relief washer assembly is discarded and the other parts have clearance holes drilled or enlarged in them as necessary to clear the nipple. Solder the pressure backup washer squarely to the pipe nipple and install the pressure washer with Super Glue and the pipe nut. This should all seal down to the inner shoulder of the filler neck. Take the tire stem and remove the valve so it can be heated to remove all the rubber. Then drill a hole into the pipe fitting to allow installation of the valve stem and solder it in place. When you are done you may install the gage in one side of the fitting and then the prepared pipe nipple with the sealing washer assembled onto it is laced through the spring seat, spring, upper spring seat, and the balance of the parts and screwed into the fitting. One of the objectives is to maintain the spring pressure unchanged so as to keep the blowoff pressure the same. Washers can be added under the spring experimentally to raise the blowoff pressure but this needs to be done with caution. No more than 20 PSI is recommended. If everything passes inspection then install it onto the radiator and gingerly add air pressure. The gage reading should slowly rise and any leaks should be easily located. If it fails to hold pressure in the tester then check for leaks at the soldered joints and be sure that the sealing washer is sitting squarely into the neck. While this device will not test the radiator cap it will test everything else in the system and is far less expensive than the $90 and up that the pro instruments cost.