Does anyone know of a reliable eye knot that is simultaneously post eye tiable (PET) and tiable in the bight (TIB), other than variations in the lock on the bowline version shown in the first image below (made with S chirality on this occasion)?
I think bowlines can not generally be tied in the bight through a tarp grommet or around a post (at least not without passing the bight around the entire tarp or the entire planet in which the post is embedded, which is impractical).
There is a practical reason to ask this: for emergency roof repairs, tarps are commonly rigged using lines tied at the corner grommets by a bowline, and reeved with half-hitches through the side grommets for strength. Then the corners can be anchored (tied down) with lines of the required length (each connected by a bowline through the bowlines). Maybe the second photo below will be better than my words. This gives a very strong rig, but on a large tarp the rigging lines are long, so threading a bowline on a corner near the centre of a line is slower than desired. Tying these corners by an eye knot on the bight could be an important time saver. But the knot must be easily tied through a tarp corner grommet. Ideally it should also resist intermittent tail loading at 90 degrees. After all, we are talking about the corner of a tarp on a roof during a storm.
This bowline does not need any lock if the 3rd eye is made about the same size as the other two and the anchor line mentioned above is passed through all three eyes, though this may be error-prone (3rd and 4th pictures below, made with Z chirality). I could not find this form in ABOK, but it is shown by it is shown by Svensson (1940) as Fig 51, Day (1947-1986) as 67E, and Warner (1992; where it is called the triple bowline) as 435. Although Day secures the tail (for a triple end loop in 67F), I think it is either-end loadable when tied in the bight, as pictured below.
I am aware of methods that use a slipped hitch (ABOK 1873) or a karabiner toggle (ABOK 1867), but they are not secure with tail loading and/or consume extra equipment.
Any suggestions?