Without using any custom modules
Drupal core doesn't have any such feature. So if you don't want to consider using a contributed module, the only options you have is to:
- Write a custom module (or further enhance the custom module you already have for it).
- Add something like a javascript to the theme(s) you're using.
- Wait for a future release of Drupal (core) that may include such feature.
- Consider using a contributed module (e.g. as further explained below).
Using the Javascript Timer module
The Javascript Timer module (available for D6 and D7) seems to be a possible answer to your question. Here is a quote from its project page:
... provides a timer API that can hook HTML elements to javascript widget objects. This is useful if you want a moving timer/clock or a widget that updates every second. It comes with widgets for a count-down timer, a count-up timer, and a clock. It uses jQuery and a single event loop to handle as many timers as you need on a single page.
Its Readme.txt file contains various examples, both Inline HTML Examples and PHP Input Format Examples.
Comment #4 in issue #1195560 contains an interesting comment that may help to get you going:
It allows for redirecting to a new URL or refreshing the existing page.
On the setting page it is called "Timer complete redirect". If you use a "redirect path" of <reload>
it will just reload the current page.