Legal situation with traffic lights at on-path cycle lanes.

Similar situation inbound opposite the Gallopin Green pub, just before the traffic lights and bus stop, there is a sign which says "pedestrian priorty area" but I can guarantee that most cyclists never see it given the speed they are going at that point and the abuse they give to pedestrians who dare get in their way.

Certainly the triangle at the end of the cycle track indicates that anyone leaving the cycle track must yield to anyone on the shared track. But once you are on the shared track, there is no implication of priority or yielding. I see nothing in what you've pasted above to indicate that bikes, pedestrians or wheelchairs users must yield to anyone else when using a shared lane.

Same as the triangle at the end of a bus lane tells the bus that they must yield as they leave the bus lane, but once they have left the bus lane, they have the same priority as the other traffic in that lane.

Ah jaysus, I totally skimmed that.

Splitting hairs, I can't find any specific legislation stating an obligation on cyclists to yield to pedestrians, though newer regulations may have included that.

Very simple - Cyclists and pedestrians shared area from this point.

Exactly as depicted.

I just showed it to a 10 year old kid. They said it means bicycles and people walking can use the path.

So a 10 year old could say on the spot what the sign means, and you can't?

They understand alright - they just prefer to ignore the signs 😁😂😁

I wonder are you playing an odd game of semantics? It doesn't say anything about cycling on a footpath. What magicbastarder's link does explicitly say is that there are road signs for "shared spaces". It's probably safe to assume that the road sign was created because these shared spaces actually exist in the real world. Are they "footpaths"? If you prefer that they're not named as such, I'm sure that's fine.

There's one just outside my place of work, and it's obviously in place because the road at that point is too narrow to allow for two segregated tracks. It only lasts a short distance, then reverts back to footpath and cycle path side by side

Right, so you are playing some sort of silly game.

The sign exists. It's in various locations around the country. A description of the sign exists. It was posted above.

The area in which the sign post is placed is designated as a shared space for both pedestrians and cyclists.

It has been pointed out that this is considered less than ideal, and should only be used where it's not possible to segregate the two.

The sign does not assign priority, but general common sense would say that cyclists cede priority to pedestrians in this space.

Of course, you're absolutely free to ignore all of this and continue rambling on about cycling on footpaths

Here's a document created by the Dept. Of Transport, Tourism, and Sport. It deals with Regulatory road signs that may legally be used in Ireland.

On page 43, the sign is listed, along with its meaning. In case you can't access that, here's a screenshot of the relevant section...

In case you can't read that, here's the relevant text

5.18.3 The sign for Pedal Cycles and Pedestrians, RUS 058, prohibits all vehicles except pedal cycles from using the identified track. The sign indicates that pedestrians, wheel chair users and cyclists share the track, and there is no physical or visual segregation between them. It should only be used in exceptional circumstances, where it is impracticable to provide segregated facilities and cyclists shall yield to pedestrians.

The text highlighted in bold was done by me, as those two pieces should answer your question

Finally, here's a picture of RUS 058, the sign in question

Well you are just wrong about the shared space. 100% legally wrong.