Sussex posted 156-8 in their 20 overs before heavy rain left umpires Steve Gale and Rob Bailey with no option but to abandon the game.
In the event, a point apiece satisfied neither team. Beaten in their opening two matches, Sussex needed victory to give their South Group campaign lift-off, while Gloucestershire required the points to close the gap on leaders Hampshire.
Having seen his side lose their opening two matches to Glamorgan and Hampshire when chasing, Sussex skipper Taylor did not hesitate to bat first when winning the toss.
But Gloucestershire struck a potentially crucial blow in only the second over, David Payne drawing a miss-timed pull shot from in-form Luke Wright, who was brilliantly held by Benny Howell on the run at deep mid-wicket. Having contributed a hundred and a 50 in his previous two outings, the England batsman made just two on this occasion.
Chris Nash gave the innings much-needed early impetus, striking two fours and a couple of big sixes, one over square leg and the other over cow corner, as he rushed to 33 from 22 balls.
But Thisara Perera made an immediate impact on his Gloucestershire debut, the Sri Lankan all-rounder dismissing Nash with a leg-side strangle, the opener edging a catch behind to Phil Mustard as Sussex slipped to 42-2 in the sixth over.
Having made a good first impression, the new boy then blotted his copybook three overs later. Sussex skipper Taylor had scored three when he was inexplicably dropped by Perrera on the mid-wicket boundary off the bowling of Howell with the score on 52-2.
Ben Brown threatened to cut loose in harvesting 30 from 22 balls, only to then sky a return catch to Howell with the score on 80 in the 11th over.
Fortunately for the visitors, Taylor made good his earlier escape, raising an unbeaten 47 from 40 balls and striking three fours and a brace of sixes. But he lacked middle order support and Gloucestershire seized the upper hand in an eventful 17th over, during which the visitors lost three wickets without adding to their score.
Laurie Evans never really got going and was pinned lbw by Chris Liddle for nine. When South African all-rounder David Wiese was caught behind off the next ball without scoring, Liddle was on a hat-trick against his former county.
England bowler Chris Jordan dug out the hat-trick ball, only to attempt a notional single and be run out by Perera, who scored a direct hit from mid-off as Sussex subsided from 120-3 to 120-6.
New batsman Jofra Archer did his best to redress the balance thereafter, chancing his arm in cavalier fashion and helping himself to 22 runs off the penultimate over, bowled by Liddle.
The West Indies Under-19 international helped himself to a quartet of fours to apply belated pressure and Liddle was removed from the attack after sending down two beamers.
Much to the relief of Gloucestershire supporters in a sell-out crowd of 5,000, Archer perished in the final over, in pursuit of a big six over cover. George Hankins athletically parried the ball just inside the boundary rope and Michael Klinger was on hand to take a startling catch just off the ground.
David Payne then removed Will Beer for a duck to finish with 3-13 from three overs, leaving a frustrated Taylor three runs short of his fifty.