How do I fix audio issue on Dell Inspiron 3585?

I have been trying to fix an issue with the audio connection on my Dell Inspiron 3585.

The issue is that whenever I plug in headphones the audio doesn't switch to them.

I have tried going via dell however they were unhelpful and insisted that it must be drivers and that I should update them. however when following their instructions it simply failed to update and that was the end of it.

If anyone has a better way to update drivers please answer.

I believe the issue may be the switch in the back of the audio jack that detects when it is plugged in (Im assuming this is how it works, I have seen this used before). I have tried to find a pinout for the connector however no luck, also the connector is mounted from the other side of the board which may complicate diagnostics.

If anyone knows where I can find the pinout for this connector I can determine if this is a software issue or a hardware issue.

Also if this is not the correct place to ask this please point me in the right direction.

It's probably a switched jack, though I can't find a schematic for one.
I can find replacements but they're sealed units, can't see inside…

You can get these for $£€ 10 - but for less than that you can get a can of contact cleaner, which will come in handy more than once.
Power the computer down, remove the battery, then spray in the jack socket & manoeuvre the plug in & out of the socket [gently] a dozen or so times.
Allow an hour to evaporate off before use.