I think one way of describing the result is that the bond in BeX+2? cation is a resonance hybrid of two possible pi bonds. Each pi bond has a bond order of 1 so the resonance hybrid structure has two partial pi bonds. But then can it further be in a resonance hybrid of different rotations and so be an even cylinder?
I guess if you wanted to be silly you could say that that the electron configuration for each beryllium ion is like:
[↑↓]2s[↑|](2p)2[]2p
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