How much time does it take l-tyrosine to begin to have an effect taking it everyday? does it takes a while like an antidepressant?

Depends: It needs to be absorbed. It needs to be converted by Tyrosine Hydorxylase to L-Dopa. If you have iron deficiency the enzyme Tyrosine Hydroxylase may not work (iron is a co-factor for this enzyme) This is how Iron deficiency leads to Restless Leg Syndrome (Its called Ekbom Syndrome if due to iron deficiency) Another couple of enzymes have to come into play to produce nor-epinephrine and / or 5HT.