We don't tend to refer to "dedication" in this context. Non-exclusive probably does mean part-time, in practice, but the terms are not in principle synonymous so I would do it literally.

"Except as otherwise provided in the preceding sentence, a Director employed on one specified program may not be required to perform services exclusively for the Company until the first day of rehearsal.
However, the Director employed on a non-exclusive basis shall in any event be available prior to the first day of rehearsal to meet the reasonable requirements of the Producer and to perform the directorial services for which he or she is employed."
http://www.dga.org/~/media/Files/Contracts/Agreements/2011FL...

"The document specified that plaintiff's duties were to be "non-exclusive" and that he would "devote such time [to the Center] as [might be] necessary to complete duties." [...]
His memorandum now asserts that his August 2000 proposal for a five year, non-exclusive employment contract at $150,000 per year plus other benefits should be regarded as an offer "
https://casetext.com/case/rosoff-v-mountain-laurel-center-fo...

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Note added at 43 mins (2014-12-30 20:57:18 GMT)
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Sorry: I quoted the wrong bit from the second reference. I meant to put this part:

"Plaintiff's August 2000 term sheet went to considerable pains to ensure that he was proposing employment only on a non-exclusive basis and that he would be obliged to devote no more time to the job than was required by his duties. "