Minecraft: 1.12.2
Forge: 14.23.5.2859
Mowzie's Mobs: 1.5.8 (no other mods are used, except JEI which is unrelated)

The sun's blessing effect lasts forever and displays as a status duration of "xx:xx". This is not correct, as it should show only 59:59 at most, as indicated by the in-game descriptions.

This is not a Mowzie's Mobs bug. This is vanilla Minecraft behavior when status effects are longer than 1639 seconds. Try it yourself with a command - it'll show the xx:xx

This doesn't mean the status effect is infinite. If you leave the game running, the effect will run out.