I suppose it's the coincidence of the DOB on the death entry being in Q2 1921 that makes it interesting. If you input 29 Apr 1921 to the 1939 Register, you don't get any returns for STIMPSON and only three for Jess* (females). Two have maiden names and married names (not STIMPSON); one has sole surname ARMSTRONG and no DOB on the transcription. As Rosie pointed out, Jessie could still be living and not in the 1939 Register but, if she's the lady who died in 1998, you'd think she'd be an open record by now. But I can't find a male STIMPSON marriage to a Jess* to account for her either, not that it means there isn't one, just not found one.
A bp record may give DOB to check against but can't find Gainsborough records for that time period on-line, and failing miserably with searching the Lincs to the Past website
There's a marriage for Bertram H HAYNES and Jessie STIMPSON in Q4 1843 in Abingdon with no obvious children for them. There's a Bertram H HAYNES in the 1939 Register in Birmingham born 1897, and looks to have died in Birmingham in Q4 1968 - but there's also two Bertram HAYNES (no middle initial) in 1939 as well - born 1891 and 1922.
LDaw is probably shaking their head and saying 'yes, been there...'