I'm afraid I know nothing about UNIC, and Googling the web doesn't reveal much either.

It houses a Landeron 4750 movement that is marked "A. Reymond LTD". This may be "Auguste Reymond"

Note: For details on the use of modern batteries in Landeron 4750/4760 based watches, please see the relevant page in the Landeron section of this site.