[wildfyr]

the NMR of hydrolyzed or dimerized TBDMS is pretty characteristic.

[Babcock_Hall]

The integrals of the tert-butyl methyl groups versus the methyl-Si groups is about 2 to 1, versus 1.5 to 1, ideally.  There are peaks downfield, which indicates that this is not a pure fraction.  But I suspect that one component of this mixture is indeed (TBDMS)₂O.