In Hungary people don’t clink beer glasses. Legend has it, that when Hungary’s 1848 revolution against the Habsburgs was defeated, the Austrians celebrated in Vienna by toasting and clinking their beer glasses. Hungarians vowed not to cheers with beer for 150 years. While that time frame is over – Hungarians still don’t ‘cheers’ with beer.
Nevertheless with any other alcoholic beverage like wine or pálinka it’s considered rude not to look the other person in the eye when saying cheers (‘egészségedre’). People will literally have their eyes wide open and protruding as they clink glasses to make sure you know that they’re looking at you, and that they know that you’re looking at them.