Fish go where the food is and with the whitefish spawn yes burbots will be in the shallows but mainly at low light conditions so fishing the shallows, from sun down to sun up is best for Burbot till about mid January then when they start their spawn they are there at any time till late march.
Remember they are a predatory fish so aggressive bottom bouncing, with large
Glow spoons or jigs works awesome also use fresh bait...(Everyone says use old smelly bait but whats more attractive to you, Fresh pizza? or 2 week old pizza?)
Make sure your hook is on bottom or as close as can be and the burbot will come along and bump it with its barb under its chin to "smell it" eventually it will suck it in, personally i catch majority of my ling on tip-ups.
i usually try and target areas where i know i have caught them before, and seem to have decent luck, also they tend to school up so if you catch one, get that hook down fast cause often a second or third one near by.