A drawer slide part for Brookhaven Cabinets

This looks like a cabinet spacer. See our 32-339, 32-334, 32-352B, 32-350 or 32-355. Look over their dimensions and see if one of these spacers seem to match what you need.

I am afraid we don't have another option for these drawer spacers other than the ones listed. You could try drilling new holes to mount them, if all else fails. Otherwise, a local hardware store may be a better bet. Apologies we can't be of more help. 

I'm afraid without seeing your original spacer, there's no way for me to make a confident recommendation. However our 32-339 has a 1" depth, same as your original. Is there any reason why this won't work for you? Depth is the most important dimension. Everything else can be worked around in my experience.