There is some evidence, from some old literature, that using para-dichlorobenzene for ectoparasite control could cause residues in eggs. (see reference below)  However, this was close contact exposure.  I could not find any information as to the effect if they were distant with a wall between.  However, nothing was noted in the abstract that even with close contact any of the birds were sick, in fact they continued to lay eggs.  However, this compound is highly toxic if consumed by the birds.

Residues in Hen Eggs from Vaporizing Insecticide Tablets

Prayoon Deema,

Edward C. Naber,

George W. Ware

Journal of Economic Entomology, Volume 58, Issue 5, 1 October 1965, Pages 904–906, https://doi.org/10.1093/jee/58.5.904

Published:

01 October 1965

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Abstract

Experimental insecticide tablets containing lindane, paradichlorobenzene, and dichlorvos, designed to control chicken ectoparasites by vapor action, were attached to the wire floor of individual battery cages. Eggs were collected at intervals and assayed for lindane by a colorimetric method and by electron capture gas chromatography. Lindane was found in the yolks by both methods, reaching a maximum after 20 days' exposure. Maximum residues detected were 0.13, 0.24, and 0.33 ppm lindane for 2, 4, and 8 tablets.