The easiest, and quickest technique: Just put a bead on your 'top' frame wire! It's quite likely you already have boxes of beads for the narrow-width 'gaps'. You may not have a large enough bead at hand for a wider gap - but we'll address that problem in the last technique.
The bead should be symmetrical and center-drilled. A round bead is perfect, but you can also use a squared bead*. Locate a bead that is twice as wide as the width of your weaving 'gap'. For example, if you want to have a 4mm gap, use an 8mm bead. Only the bottom 'half' of the bead will be doing the actual spacing. The other half will be above the wire, out of the way of your weaving.
Slip the bead on the top wire. You may put it on the bottom wire, but it is more likely to interfere with your weaving when in the lower position. Note that the bottom half of the bead just touches the bottom wire - perfect! (Spoiler alert: The bead in the photo wasn't quite large enough - but the only bead I had on hand to illustrate the technique.)
*If all you have on hand is a squared bead, double-check its actual width with a piece of wire, from the center of the bead, around the angle, and then around to the center of the other side. Choose the squared bead size accordingly. Note that the dimension of the gap may change if you don't keep the square bead perfectly straight and aligned with the wire frame. (If it turns a little bit, you will be creating a wider width, because the width across the bead, from top half to bottom half, including the corner angle, will be greater than just a 'side' dimension.)
Start weaving. Keeping the bead's edge riding along the bottom wire, just in front of your weaving, so you can continue to double-check that you are maintaining the proper width.
The bead will slide easily as you work. You may want to bend a little curl on the end of the wire that holds the bead, to keep it from slipping off accidentally, then snip off the curl when your weave is complete.
Pro Tip: Tip: Hold the previously woven end tightly as you bring the wire over the gap, to make sure that the wire is reasonably tight as you make your first 1-2 coils on the top (or bottom) wire. Keeping the correct tension on the wire prevents 'sagging', which allows the wire to curve a bit, and also creates a place for variation in the width to occur.