Surprisingly, this isn't a particularly bad option.

Metallic mercury is not very reactive, it'll just pass right through your system (it was used as a laxative by ancient Romans). It's only once mercury has formed organomercury compounds that it gets really toxic and eats your brain.

Methanol is somewhat toxic but has easy and effective treatments to prevent it from harming you. Amusingly, one of the easiest treatments is to just drink a whole lot of ethanol as well. Methanol itself isn't the real problem, it's the toxic byproducts that are produced when the liver metabolizes it. By drinking a whole lot of ethanol you can keep your liver occupied metabolizing that instead, until all the methanol has left your body by direct means (sweat and urine).

Disclaimer: Don't rely on the internet for medical advice. If you've drunk a glass of methanol and mercury in real life call the local poison hotline immediately. I am not a doctor and I'm mostly just rambling from memory.