This Sweet Sound Mojo Vibe is probably the best reproduction of the classic 1960s Shin-ei Uni-Vibe. It's got all the sounds you need as well as modern capabilities. No velcro on the back! Does not come with the original box.

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From the interwebs:

The Sweet Sound Mojo Vibe is a compact, boutique guitar pedal designed by Bob Sweet that faithfully recreates the rich, swirling optical circuit of the classic 1960s Shin-ei Uni-Vibe. Key Features & Design

• Authentic Optical Circuit: Uses a genuine light bulb and photocell configuration to deliver the lopsided, throbbing wave-like modulation heard on classic Jimi Hendrix and Robin Trower tracks.
• Controls: Features dedicated knobs for Volume, Intensity, and a large Speed knob designed for easy on-the-fly foot adjustments, plus a toggle switch for Chorus (Uni-Vibe sound) vs. Vibrato (pitch-bending mode).
• Expression Control: Includes a 1/4" stereo jack to hook up a passive volume or expression pedal for foot-controlled sweep rates.
• Internal Buffering & Power: Features true bypass, internal 18V DC voltage conversion (from a 9V DC source), and an internal DIP switch to engage an FET buffer for modern, high-clarity setups.