If indeed the Excelsior BigX 1917 picture is a match for your bike, there was a 'military' version of this bike in the late teens 1917-1919 - although they weren't actually sold to any armies, they didn't get a contract, they were just painted to look military.
They can usually be dated by the frame number, stamped under the seat, and are quite collectible, all electric models especially so. Restored ones can bring mildly hefty prices, although parts are tough to come by to get them perfect - most you see are usually cobbled up remnants. However, fairly original complete intact ones are surprisingly common, for a make that didn't sell anywhere near the volume like Indians or Harleys.
As mentioned though, Indian Harley etc also did bikes that are reasonably similar to look at, its the fine detail that distinguishes them - and the specific year of manufacture.