Depends on the geography and hydrography
Of course trade stops between the opposing sides of a war but how does that affect any neutral parties?
If a neutral has a land frontier with belligerent and there is an economic or strategic return on engaging in commerce, they will; obvious example is the USSR and Germany in 1939-41.
Otherwise, if trade requires maritime commerce, it really depends on which belligerent has the advantage at sea.
Neutral rights in terms of trade during wartime have varied greatly over time; given the "pre-1900" status, you really need to narrow down the time frame and (roughly) the region of the world your belligerents call home...
Best,