barbed wire, covered then left bare
“Something wrapped all of my past mistakes in barbed wire”
“Where's that man who'd throw blankets over my barbed wire?” — tolerate it
Read together, invisible string gives the barbed wire something wrapped around it, and tolerate it asks where the man went who used to throw blankets over that same wire. In invisible string the covering is given, protection or restraint depending on which host you follow; in tolerate it the speaker asks, in the song's own bridge, where the covering has gone, and the question reads as bitter rather than merely wistful. The same image is offered, then withdrawn.
Patreon comment by Cara M on "Time's Mystic Meandering in Invisible String", the only reading offered across both songs as protection given and then withdrawn, and the only one to hear the bitterness in tolerate it's own question. Convergent reading also offered by Amos McShamus (Patreon, the wire as a guarded heart he softened, with a reply from Jennifer agreeing), @leesajohnston7871 (YouTube, her mistakes making her hard to love) and Katherine Heaney (Patreon, in a reply, the wool and the blankets as the same covering). The pairing alone, without this argument, is also offered by @SeidSays227, @Gabri.elleFerre, @kiroisbreathing7796, @LK-lz6lk and @nogaglucksam5783 (YouTube) and Karen S (Patreon, with replies).