Here is how I would approach this saw if it were mine.
1) I do not believe your problem is the carb. If the spark plug is not throwing a fat blue spark, I would replace the coil.
2) Your vac tester will not come with a plug to seal the intake hole behind the carb. I use a flat plate with a piece of inner tube behind the plate to seal the intake or a rubber stopper trimmed to fit. Your exhaust port on the cylinder must be sealed as well. This can be done with a piece of inner tube behind the muffler, then tighten the screws. Plug the van gun into the impulse port on the saw frame where the carb impulse line plugs in. Pump the saw down tp approx -7 psi. If the saw does not hold and leaks off before 10-15 seconds have passed, set the vac gun on pressure and pump the saw up to +7-10 psi and dunk the entire saw in a sink or tub of water and watch for bubbles. The bubbles willl most likely indicate the leak point.
3) Regardless of the vac test, I think I would take the saw down to the level of removing the cylinder. This is a relatively easy task mechanically on the 026 and you will learn a lot that will be helpful later. This will also give you the opportunity to closely inspect all rubber lines and boots, you can replace your cylinder gasket . Pull the flywheel and check if you have a broken flywheel key and check the gap between the magnets and coil contacts. At 125 lbs compression, that is runnable but that saw should throw 140-160 stock. You can replace the rings when you have the cylinder off and clean up the piston,check for skirt wear, clean up the cylinder and check for scoring. This will require a ring compressor and a set can be had cheaply($10) from site sponsors and auto parts houses. Remember your clutch is left hand thread.
4) Take advantage of this opportunity make the saw a useful learning experience. They can be frustrating at times but usually good solid diagnostic procedures will lead you to the problem. The 026 is the best training saw out there.
