Mayonnaise Shotgun.
It is difficult to shotgun a jar of mayonnaise, but if that is what you desire, here is what I recommend. The eggs present in a batch of mayonnaise have emulsified, leading to that creamy thickness, making it difficult to chug through the puncture hole at the bottom of the jar, regardless of how much suction is applied.
If you heat the jar ahead of time, the emulsion will "break," separating the oil, and creating a much looser substance, that will easily be shotgunnable. HOWEVER, do not use the microwave to heat your mayonnaise! Low and slow is the name of the game, preferably a simmering water bath. If your temperature is too high, you will cook the eggs, leading to an even thicker, less chuggable substance.
Bon appetit, and good luck!
P.S. PLASTIC JARS ONLY, NO GLASS