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hello again noah,
two thoughts -
a) that is quite a bit of exposed spindle showing in the closeup photo. makes me wonder if spindles are original to pedals. certainly a chance they may be replacements. pedals do not usually have this much exposed spindle showing when assembled. ball size should be 5/32". wonder if perhaps they got reassembled at some point with 1/8" instead.
b) since what is required is a threaded cap you might consider taking measurements of the thread and then checking with industrial supply houses and or plumbing supply resources to see if they have anything the right size.
here is a fastener supply resource which has been very helpful to me with odd sized bits -
https://www.bowlinbolts.com/
https://www.yelp.com/biz/bowlin-equi...any-berkeley-2
https://www.facebook.com/pages/Bowli...46427768722092
all best wishes with this!
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