GA4: Adding a variable parameter to an existing event

I recently created a Google Tag Manager variable for my client's website that is successfully firing. (It helps identify which client account is logged in and navigating the site without revealing any personal information.)

I would like to surface that variable as a parameter for GA4's standard "page_view" event, but I can't figure out how. Has anyone had luck with this?

I can create a whole new event via GTM solely to surface the variable, but I would rather pass it as a parameter inside "page_view".

I have been trying to figure out a way to identify the variable in the "New value" field, but it doesn't seem to work.

Suggestions that don't involve creating an event solely for the variable?

I would post that in the Google Forums and hope that Simo Ahava takes a bite! I know only that GA4 event configuration is a different tag, but that possibly has nothing to do with what you are asking.

@GlynMusica Yeah, the tag part I have figured out, but thanks!

I'll try the Google forums as well in case no one here has an answer.