The LT I'm rejuvenating has this.  What does this mean?  Has the ABS relay gone kaput?

I'm not an expert on ABS, but did have a similar problem.  Are you sure the ABS reset switch is working properly?  If not, it will not only not get the ABS warning light to flash when there is a fault, but it will also prevent clearing a fault from memory. 

And to answer your question, yes, there are two relays and one is for the alarm light, and it could have a problem.  I had one fail on my K75RT with ABS 1.