Not a ROVER

Unfortunately, there is only one image of William Starley's "Eye-Opener" - from the advertisement. In many sources it is mentioned, if it is mentioned at all, as ROVER. But ROVER never operated under the name Starley in the 20th century. Only further"digging" in documents establishes a connection to William Starley - via the British patent GB4418 from 1903, the French counterpart FR 318.842 or the American counterpart US 746.652 on the same subject.

The patents mentioned are concerned with a "motorcycle with worm wheel drive and gearbox". The three patents were granted to James George Accles, Frederick Henry de Veulle and William Starley.

No documents could be found for the motorcycle itself. It is only reported in a report about the Stanley Show 1902 as follows:

The Starley Motor-bicycle. A new motor-bicycle appeared on the stand of the Houk Automobile Co, Ltd., late on Saturday. This was the Starley motor-bicycle for 1903. The frame is specially designed to take the engine, a tube runs from the top of head to a point on the strut, just above the bracket, and two twin tubes run from bottom of head to same point: the vertical engine is carried on an extension in front of the bracket. Each of the three triangles of the frame contains a tank, the forward one holding the oil, the tank in the main panel containing petrol, and a wooden box between strut and back wheel carries the coil and accumulators. Spray carburetter is fitted, warmed by hot air from the front of the cylinder. A drip-lubricator is fitted, the drip being variable by means of a lever on the oil tank. The low tension wires are contained in the frame tubes; this makes for neatness. A gear-case is fitted to this machine.

Another source complements this information somewhat:

Starley's Ltd of St John's Works, Coventry
1903 Starley was a motorcycle invented by W. Starley of Coventry (presumably William Starley), and built under licence by the Swift Motor Co. It was shown on Houk's stand at the 1902 Stanley Cycle Show.
This machine differed from most in that the single-cylinder engine was mounted transversely to drive back through a two-speed gear and worm and wheel. The wheel was on a countershaft that drove the rear wheel by chain.
The engine construction was also different as the cylinder was held down by a large ring, which screwed on to the crankcase top, and a one-piece over-hung crankshaft.
The whole design was highly complex and nothing further came of it.

The illustrations from the patent specifications are identical. The documents of Swift Cycle Co. do not contain any reference to this motorcycle.