Accessible tooltip with links

I'm working on an accessible input component with built in tooltip. I've managed to create a solution that seems to work fine for people with limitations — whenever user focuses that input with keyboard, not mouse, if he doesn't start typing within half a second a tooltip appears and screen reader reads it.

However there came some cases with links inside tooltip, meaning user must be able to navigate inside a tooltip cloud and focus links.

What could be the pattern to use here that would be intuitive to the user? Using tab to navigate inside the cloud might not be ideal since one might expect it to move to the next control on the form. Using arrows to navigate focusable elements in the cloud seems not that intuitive and it gets in the way of autofill.

I was hoping maybe somebody here has experience implementing such a case and could share his insights. I know one way would be to keep hints clear of links and show such info explicitly on the page, but that's outside my control.