If you go to Findmypast you will find records for a Frederick Billett - the DOB year is out but not sure how they calculated this is it based on age at enlistment or actual birth year? There were no other Frederick Billetts born in Taunton at that time. Anyway you can buy credits online it may have some information that is relevant for you.
British Army Service Records 1760-1915
Place of Birth: Taunton, Somerset
Collection: WO96 Militia