Why would a solution of FeCl2 appear brown/yellow sort of like FeCl3?
The yellow/brown color you are seeing in the solution of $\ce{FeCl2}$ is due to formation of various types of hydrated iron oxide and not iron(III) chloride. They may include both the anhydrous($\ce{FeOOH}$)  or the monohydrate($\ce{FeOOH.H2O}$) often referred to as ferric hydroxide($\ce{Fe(OH)3}$). They are generally yellow to brown in color. The reaction is given here:
$$\ce{4FeCl2 + 6H2O + O2 → 4FeO(OH) + 8HCl}$$

Reaction between iron chloride (II), water and oxygen(moisture) to form
iron metahydroxide(Iron(III) oxide-hydroxide) and hydrogen chloride. The reaction takes place at
reflux.

Moreover, if you further heat iron chloride in oxygen at 450-480℃, iron oxide will form.
References(all pdf links)

http://www.jieas.com/fvolumes/vol081-5/3-5-11.pdf
http://www.gfredlee.com/SurfaceWQ/StummOxygenFerrous.pdf
https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/77056/1/chd061_5-6_335.pdf