The only thing that I was able to find so far is an addon called Advanced Member Tooltip.
http://www.esoui.com/downloads/info1380-AdvancedMemberTooltip.html
It is supposed to show the number of days since a member joined a guild, and the amount of gold the member has deposited and withdrawn from the guild bank. After reading the few comments for the addon, it looks like it may not be working 100% correctly. It is also a little outdated: Updated: 02/06/17. Perhaps someone could update it or fix the mistakes.

I've never used it, so I don't know if it still works or if there are any issues with the calculations, but it's the best thing I could find as of now. The guilds that I've been in usually used notes to keep track of join date unfortunately. It would be quite useful if join date or days in guild was part of the default UI.

If it's something that you don't mind using a note for, but you'd rather not put it in the public notes, you might try something like FCO Notes. It lets you create your own personal/private notes for guild members.
http://www.esoui.com/downloads/info1065-FCONotes.html
I did use that addon back when I was still actively playing around 6 months ago and I didn't have any issues with it. It was last updated 3 months ago, but that doesn't mean it doesn't work.