Per the OED, dowse is a variant spelling of both douse verbs. They do not know where the water-seeking verb came from. I’ll give the nouns first.
Forms: Also 16 douze, 16– douce, dowse, 18 douss.
Etymology: < douse v.¹
A dull heavy blow or stroke.
Etymology: perhaps subst. use of douse, douce adj. sweet.
A sweetheart; a ‘dear’. Also ironical.
Forms: Also 16– dowse, 17 dousse.
Etymology: Of obscure origin: known only from 16th cent. In sense 1, perhaps related to Middle Dutch dossen, or early modern Dutch doesen to beat with force and noise (Kilian): compare also East Frisian dossen to beat, strike, punch, knock, and German dialect dusen, tusen, tausen, etc. to beat, strike, butt (Grimm). Senses 2, 3 may be the same word; compare ‘to strike sail’; sense 4 is more doubtful, and may be distinct. All the senses belong to the lower strata of the language.
- † trans. To strike, punch, inflict a blow upon.
- Naut. To strike (a sail); to lower or slacken suddenly or in haste; to close (a port-hole).
- To put off, doff.
- To put out, extinguish, dout (a light).
- To throw down, table (money): = doss v.¹ 2.
- To ‘shut up’, stop, cease.
Forms: Also 16 dousse, dowsse, douze, 16– dowse, douce.
Etymology: Appears c1600: origin unknown; perhaps onomatopoeic; compare souse. It is of course not impossible that it arose out of douse v.¹, though connection is not obvious.
- † trans. To plunge vigorously in water, or the like; to immerse with force. Obs.
- To throw water over; to water, to drench.
- intr. To plunge or be plunged into water.
Forms: Also dowze, douse.
Etymology: Derivation unknown; apparently a dialect term.
intr. To use the divining- or dowsing-rod in search of subterraneous supplies of water or mineral veins.
• dowsing n.
• dowser n. /ˈdaʊzə(r)/ one who uses the divining-rod, a water-diviner.
• dowsing-rod n. the rod or twig used by dowsers.
All these entries are from the online 3rd edition of the Oxford English Dictionary, but also appeared in the 2nd edition from 1989, with an earlier version also appearing in the New English Dictionary (that is, the 1st edition) of 1897.