Half as long but still in the center? .. (I would insert an image here but apparently It Is Not Allowed Using Safari. .. Not that many people using Macs, eh?)
let a = your column width
let b = your row height
Create a new Dash stroke style; the pattern length should be sqrt(a² + b²). Drag out the dash marker to half. Make sure "Adjust Corners" is set to None, 'cause else InDesign will attempt to draw two segments.
(I actually tried to make the dash just appear in "the center" of the pattern, but you have to start with a filled segment. So I did the inverse and tried Line in Paper Color, Gap in Black; but then I got an ugly outlined line. .. Again, sorry, no image today.)
I can't thank you enough for you help. I had to play around a bit to see the right direction, but it works beautifully!