This route is strictly the traverse between the highest and second highest peaks on Pichincha so the approach is whatever route was used to the first summit.
This is a wonderful high traverse across the Pichincha massif. It is excellent acclimatization and can be done in a day although spending a night out above 4,300 meters is better than returning to Quito at only 2800.
This route is popular enough with Ecuadorians that there is a trail between Guagua and Rucu. It is a little difficult to follow through the vegetation between Rucu and Padre Encantado but does not pose any serious problem. You will need 2-3 hours from Rucu to Guagua and 1.5 - 2.5 for Guagua to Rucu. The description is Rucu to Guagua which is my recommendation. See Dangers below.
From Rucu's summit you can see the beginning of the route traversing below some cliffs and along the ridge to Padre Encantado. From the summit descend the standard route through the sand. Stay to the left and look for the sandy notch that provides easy access to the other side of the ridge. Desend the sandy slopes as best you can and meet the path below the cliffs. There is a nice cave here as a bivy option.
Follow the path toward the imposing cliffs of Padre Encantado. The path crests the ridge near P.E. and drops down the other side. Continue the traverse on the opposite side to the ridge between Guagua and P.E..
This ridge never goes below 4,300 meters so there is not a lot of elevation gain and loss. The route ahead is plainly visible (sans clouds of course). Take the ridge to the northeast slopes of Guagua. Ahead is a sandy slope with a climbers use path slashed across the upper section. This is unpleasant hiking but ascend the sand to the path and take the path to the rim.
You are deposited on the standard route immediately below the summit. Take the gully (2-3 class 4 moves) up and then rock hop to the high point which is now behind and to your right.
Standard hiking gear will suffice.
It is tempting to do this from Guagua to Rucu and then descend back down into Quito. I do not recommend this because the lower on Rucu Pinchincha that you go the more exposed you are to robbery and assault
. That particular attack in December of 2007 occurred at around 15000 ft / 4500 m so it was well above the cable car station and not low down at all. With that in mind I would not recommend climbing this peak at all unless you are a group of people with machetes.
Sadly this same sort of risk is present on all the "trekking" peaks of Ecuador including the rest of the Pichincha massif. Outside of Rucu I don't consider it a "high" risk but overall I do consider Ecuador to be higher risk than many other South American destinations. So be aware.