Your question led me to:
Pinals, RS (1988) Sulfasalazine in the Rheumatic Disease. Seminars in Arthritis and Rheumatism 17:246-259. I reproduce the introduction to this paper below:
Most physicians are familiar with sulfasalazine (SSZ) as an agent commonly used to treat inflammatory bowel disease for more than 40 years. In 1978, McConkey et al reported preliminary studies suggesting that this sulfonamide might be effective in rheumatoid arthritis (RA).1 The use of SSZ arose from earlier open and controlled trials with a sulfone, dapsone, which had demonstrable efficacy in RA, but the benefits were accompanied by relatively frequent, often unacceptable adverse effects.2 Dapsone was effective in dermatitis herpetiformis, presumably because of immunosuppressive activity. Another therapeutic agent for this skin disorder was sulfapyridine (SP), a drug with a poor record of gastric tolerance. Therefore, McConkey et al elected to try SSZ, a compound that released sulfapyridine in the bowel after passage through the stomach. Ironically, McConkey was initially unaware that SSZ had been synthesized specifically to treat RA in the late 1930s. In 1980, McConkey et al reported their open experience with SSZ in 74 patients treated for up to 1 year.3 The improvement in erythrocyte sedimentation rate (ESR), C-reactive protein (CRP), and clinical score (a global evaluation) was similar to that achieved with the disease-modifying antirheumatic drugs (DMARDs), and appeared somewhat sooner, often within 2 months. Moreover, although adverse effects were frequent, they were seldom of sufficient severity to discontinue treatment. This encouraging report led to several controlled trials in the United Kingdom and elsewhere, all confirming the efficacy of this interesting agent. The first study in the United States has been reported4 and, although SSZ has not been approved by the Food and Drug Administration for use in RA, many rheumatologists have used it as an alternative DMARD because of its availability and long record of safety and efficacy in inflammatory bowel disease.
What I have gleaned from this and a couple of papers cited there is that B McConkey, working at a hospital in Birmingham in the UK became interested in developing methods of clinical assessment of rheumatoid arthritis (RA) in the 1960s and this led eventually to the discovery that the drug dapsone is effective as a treatment but with an unacceptable level of adverse side effects. Then, to quote McConkey:
We had studied dapsone partly because of its effect in leprosy and dermatitis herpetiformis; its mode of action in those diseases may be through its immunosuppressant properties. Another drug used in dermatitis herpetiformis is sulphapyridine;it did not attract us as a contender but it is a constituent of salicyl-azo-sulphapyridine (sulphasalazine), a compound originally formulated for RA and latterly found to have immunosuppressant properties.
McConkey et al (1980) Sulphasalazine in rheumatoid arthritis. British Medical Journal 1: 442-444
(This is ref 3 in the Pinals introduction.)
So clearly there was a strand of chemical logic in the rediscovery of the drug; the only serendipitous aspect was that McConkey did not at first know that sulfasalazine was originally designed as a treatment for RA.