iPod only gets sound through one speaker

It is possible that the headphone jack has become damaged over time. You might want to investigate your options for third party or DIY repair. Replacing the hold switch and headphone jack assembly is relatively straightforward, but the process of opening up the iPod classic case is less so.

tt2

Here is an example part listing in the UK: https://www.ebay.co.uk/itm/123407532318. If you decide to do it yourself you can find plenty of guides to the process online. Alternatively search for local repair services. I would suggest that Apple's repair service for older devices is not competitive: iPod Service Pricing - Apple Support.

tt2

So now that you have ruled out it's not the headphones, it must be the ipod.

I suggest take it into an apple store or ipod repair centre.

I would suggest try another pair of headphones before ruling that out.

If you see it's not the headphones, it can possibly be something else.