I'd use SS "U-bolts", like shown below, to fit the diameter of the rail, if permanently mounting the base.
Or, if using the 'portable Go-Light wired spotlight (that I use), I used (3) SS squiqqly-type spring clamps, see below, that hold the plastic base to the rail, secured by a bungee. It takes but seconds to deploy and is only mounted when I know I will be out late and may need the light.
Now, as a 'blend' of the 2 options above, you could permanently mount the base, as the Go-Lights comes with a slide-in, snap-in base that can mount to the plastic base. Then you just slide the spotlight in when needed and plug the wire end into a cigarette lighter-type electrical port.
Go-Light portables are awesome! And if anyone needs it, I re-wired mine with a resistor in-line to the motor connections that slowed the pan & tilt to a more manageable level.
BUT ... you need to do some 'marinizing' to the wiring and unit to make it bulletproof for boat use. But, for < $100 ... it's easily doable.
Did I say I'm a 'cheap' ******* ... ??
And yes, CPG Seaboard is just like King Starboard, but around here (New England) I can typically get it for 1/2 to 2/3rds the price of starboard. Their 'sand' color matches Parker's gelcoat perfectly! Try a plastics distributor.