This has been a fascinating bit of discussion. I've 2d I can throw in.
In the good old days of the Royal Army, a Battalion was two companies, a heavy and a light Company. The Light Company was usually deployed as, if I remember the contemporary materials rightly either in skirmsih order or as piquettes. In that day, massed formations were spaced shoulder to shoulder, call that about 1m apart. The command "Open Ranks" doubled that to 2m, and then "Skirmish Order" was double that again. (I'm operating off of memory and without references here, so, apologies for any mis-statements.)
Part of Militia Drill was in creating such formations, so, having the Soldiers Open Ranks, suggested a spaced line, rather than a solid surface. More than once, it has been suggested that is where the decriptive term "picket" came to be applied to fences.
I want to remember that the USN practice of setting up radar "pickets" is a reference to fences more than any other use (but it has been many, many days since I had to pour through the planning documents from that erea, too).
Rather an interesting potential comparison, a steam picket boat, and, say, a DDR or SS(R).
USN practice is that a blue hull is a barge (for admiral's use); blue stripe is a commodore (under a burgee).