This is perfect, we have an 1863 with similar issues. Turns out the real issue ends up being the battery connectors. Wiggle them around a bit and she fires right up. I would suggest making sure battery terminals and connectors are clean.
Ours doesn't have any relay, probably contributes to the issue it has but we've always been able to get it to start up just by monkeying with the battery connectors a bit. I would install the relay as it might be a different issue entirely.
Oh, except our 1863 has the automotive-type clamp connectors, not sure what yours would have.
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147 R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)
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