Although it is not a gooseneck lamp, something like this should work well (Nichia 219 Desk Lamp Retrofit)
I used a triple Nichia 219 star from Illumination Supply (https://illuminationsupply.com/nichia-nvsl219ath1-4500k-92-cri-b10-bin-20mm-triple-star-p-160.html) and a 10 watt driver for MR16 style light bulbs (http://www.fasttech.com/products/1612/10001419/1110706-12v-1x10w-high-power-constant-current-led-driver) The driver uses the PT4115 chip and does not do PWM. You feed it 12V-30V (ac or dc) from a wall wart.
Find you a gooseneck lamp and you’re there…