On a WooCommerce shop the sales and the coupons are often run by shop managers, and until you choose otherwise only administrators can open Countdown Timer. Under Settings → Who can manage campaigns, tick Shop managers, and they get:

the Dashboard;
Campaigns: adding, changing, copying, moving and deleting campaigns, their coupons included;
Cart Timer.

That lets them put a countdown on any page, a bar across the whole site, and a coupon on every cart. Settings, the licence, importing and exporting stay with administrators, and so does the choice of who else may come in. Settings is not in their menu or the top bar, and asking for it by its address, or sending its form, is refused. Where every timer is switched off under Settings, their Dashboard says an administrator can switch them back on.

On a site that has not chosen, the Dashboard asks an administrator once: Let them in ticks Shop managers, Not now leaves administrators alone, as before. Either way it is not asked again, and Settings can change it whenever you like. A site without WooCommerce has no shop managers, so it is not asked, and its Settings says so. A choice made while WooCommerce was on is kept while it is off.

The choice is a capability, trct_manage_campaigns, which administrators always have. A role editor plugin can give it to any other role, or keep it from shop managers whatever this setting says. Changing which coupon a campaign works with also needs WooCommerce's right to edit coupons (see A coupon that works only while the countdown runs). Nothing is written to any role: switch the setting off and they lose access on their next page. On a network each site makes its own choice.