Hmmm... But what does it mean if the card works on some systems, just not one of them?
Is that a sign of the contacts on the inside?
Yes, or some other issue with the console itself (see steve's explanation above).
Can we open up the TG-16 and bend them out, kind of like what people do with Famicom/NES ports with a small screwdriver and gently raise them up?
Because, if the system works with other cards, why would raising the pins help with this card? Please explain. 
Because not all HuCards are created equal. Your "problem cards" may just have contacts that are either slightly lower or slightly "off center" enough compared to other cards to not make contact with the used and abused pins in the cartridge slot on your console. This could be due to the way they rolled off the assembly line, or it could be due to corrosion, dirt, etc. Or it could be due to some other issue with your console, such as termination in steve's case.
I have three copies of Tales of the Monsterpath that don't work on my Duo, but work fine on my handheld GT. I kept buying them because I thought I was getting bunk carts. The problem is not that the carts are "broken" in some way, the problem is that particular game was apparently manufactured in such a way that puts the pins in a position that makes contact difficult in all but the cleanest, least-abused slots.
Does anyone here repair hucards?
Apparently nothing I've been trying to say is getting through. Chances are
highly likely there is nothing to "repair."
