I bought a needle applicator bottle which can be applied very precisely. But you can get a smaller quantity. It doesn't take much, so even a small quantity, like the one from the link below, can last a long time.

https://www.amazon.com/Wireworld-DEOXIT-...ords=Deoxit+red

Apply it to both sides of the middle wafer of the HDMI jack. There are contact pins on each side.

Some of these pins (19) relate to video, some audio, others are for HDCP handshaking and so forth.
So, you can see why oxidation issues can cause either video or audio or handshaking problems.