amateur observing - Periodic behavior of Venus

Assumed a Venus year is 0.615 198 Earth years.

0.615 198 yr / (1 - 0.615 198) = 1.598739 yr = 583 days 11 hours 24 minutes for one period in mean, or roughly 19.5 months.

That's 1.598739 periods for Earth and 2.598739 periods for Venus:
1.598739 * 365.256 days = 583.95 days = 2.598739 * 224.705 days

The relative accuracy should be somewhere near 1e-5.

Since both orbits are elliptical the actual period oscillates around that mean value.