Not sure if simple entity has a gui but if you change to a an entity that does i.e lamp type you can set up custom events to open the gui when you open with default left click and close with E.

check out https://mods.factorio.com/mods/Zinal/Custom_Events for an example.

Also you could set it up so if player == player that created sign then open up the editor to change the message

But still I'm unable to auto-close this default GUI, right? So player would have to close the signpost GUI and then the normal e.g. lamp GUI?

It would be good if API authors would introduce such important method.

You can set it up to auto-close the signpost gui when the lamp gui is closed. But not the other way around. You could even take it a step further, When a player gets close to a sign with a message it automaticly pops up the sign and closes it when the get further away.

What we really need is for factorio to give use on_opened and on_closed entity gui events as well as the ability to do something like mygui=entity.gui.left.add to attach our Gui's right to the entities gui.

Yup. I'm not convinced with such hacks and the "on_entity_opened" event is kinda important here. I will wait till devs will introduce such event.

There is a post on the interface request forums for this, you should bump it up :)