Question: If I use a dual-disk enclosure that employs JBOD, would I be able to at least access and use a second disk in the event that the other fails or otherwise becomes inaccessible?

Answer: JBOD means no RAID, incuding the ‘R’ part that means redundancy unless you did this with other means.

JBOD across two disks without RAID is spanning a volume across two physical disks. ?There is no redundancy (unless your documentation tells you different – both JBOD and RAID can mean different things to different people sometimes). ?Technologies to do this include Windows “dynamic volumes” and Linux’s LVM.

In a spanned volume, if one disk goes down, data on the entire spanned volume, i.e. ALL your data, is at risk.

If you want to be able to access the volume if a disk in it fails you need some type of redundancy and pay for it with disk space, either hardware RAID or a software equivalent.