Do the prices of used video game consoles go up or down during Christmas?

Christmas & other holiday events usually don't cause any significant changes in prices because retro (5-10 yrs old) & vintage (10+ yrs old) games are a bit niche product.  There might be a slight increase with a few sellers trying to take advantage of some buyers, but it's generally unnecessary as most vintage games are already on the upward trend on the pricing curve.  Retro games might be hitting the bottom of the "U-curve" & start creeping back up.

If you checked prices on VGPC.com , you can see historic trends for platforms in general as well as individual games.

Usually the used game price doesn't drop unless the new price also does, at least in the case of Gamestop, but even then sometimes the used price doesn't change when the new price does. I've seen situations where the new copy is actually cheaper.

I'm  not sure about all families, but typically in mine we don't give used stuff as Christmas gifts.

There are often sales but Black Friday is usually better.

i would think new, modern ones will go down as they will want to boost their sales and sell more.  

if you are collecting and into nostalgic gaming, those might go up since there are less of them out there now.