I got the lamp to work! With 120v to the white when the switch was flipped, I made a couple of assumptions. First that there was no neutral in the ceiling and secondly, somewhere in the ceiling, the black from the switch is connected to the white in the ceiling. In the switch box, I took that top black wire from the right hand switch and connected it to the neutral bundle, removing the incorrect white. Now the lamp works using both the red and white ceiling wires. I don't think the ceiling black is connected to anything.

THANK YOU VERY MUCH. THE DIAGRAMS AND EXPLANATIONS HELPED ME UNDERSTAND HOW THE SWITCHES ARE HOOKED UP. I AM A BIT NERVOUS WORKING WITH ELECTRICS, AND GREATLY APPRECIATE YOUR HELP.

 

Glad you got it but you created a code violation.
You can't use a black for neutral in this situation.. There are exceptions but the apply to wires #4 and larger.

Given this is a renal and given the liability I would strongly sugest you undo what you have done and insist management install the light for you. Don't tell them what you did or suspect is wrong. Let their electrician figure it out.

 

Thanks. That's what I'll do. Man, I thought I had fixed it!