DC Power Supply for Radio

I'm looking for a reliable DC power supply for my coil tattoo machine equipment. It needs to include a rechargeable lithium ion battery that will last running at 12 volts for a minimum of 13 hours. A 1/4” jack, a voltometer, an on off button, and a panel mounted voltometer at minimum. It needs to be as small as possible for ease of travel and obviously cordless unless charging. Thank you

Requirements:
- Type: DC power supply
- Voltage: 12V
- Current: 1A, 5A, or 10A (I'm unsure about the exact requirement)

Ideal Skills and Experience:
- Experience with power supply design and specifications
- Knowledge of DC power supply units
- Ability to provide recommendations for optimal current output

Please provide a detailed proposal including your approach and any relevant experience.