Look @ it like this; the gene that you are focussing on is the sex-linked recessive brown dilution gene (d) assuming that all other genes/alleles are equal & consistent with that of the harlequin ie m^d/m^d, li^h/li^h. Drakes have two equal positions (loci) for this gene on a pair of like chromosomes because they have the two sex-determining chromosomes ZZ. But ducks only have the one position on their pair of sex determining chromosomes, because unlike the drake (ZZ), their sex-determining chromosomes aren't exactly the same but rather Zw. Only the females Z chromosome will have the locus for sex-linked d just like the drake, but the smaller w chromosome doesn't.
Now, if the drake is pure for the recessive brown dilution gene he will be d/d, but if impure he will be D+/d. If pure for d/d, then he will (if expression not masked by something else) express the brown colour, but if impure D+/d, then he won't express brown because the more dominant allele will prevent such expression. The duck on the other hand only needs one dose of the recessive brown d/- for brown to express because as per above, she can only have the one gene @ that locus on her single Z chromosome; just like your ducks are from your description.
Your so called "silver phase" drake could be pure for "not brown" (m^d/m^d, li^h/li^h, D+/D+), or he could be impure & carry hidden one dose of the recessive brown dilution gene ie m^d/m^d, li^h/li^h, D+/d. If pure for "not brown" then when mated to a "golden phase" duck (m^d/m^d, li^h/li^h, d/-) all ducklings produced will inherit the more dominant allele "not brown" from the drake so not express brown (therefore silver), but all the drake progeny will carry hidden one dose of the recessive brown dilution gene ie m^d/m^d, li^h/li^h, D+/d. However, if your drake is impure for recessive brown dilution (m^d/m^d, li^h/li^h, D+/d), then approx 50% of progeny, both male & female will express brown (therefore gold), while the other 50% progeny, both male & female will be silver; the silver males again carrying hidden one dose of the recessive brown dilution gene.
