Simon,
There is a difference between how the model works and if the timing is good to implement the model.
First, I do not believe in market timing when it comes to property. Better is to focus on the cash flow and buying a bargain. In up or down markets there are bargains and there can be property that will safely cash flow even if there is no appreciation.
Back to the question.
You would refinance the property to pull out equity to purchase the next property. Or you could choose to use other capital to make the purchase. Or you could look to obtain 100% financing (ignore the mechanics for a minute). If you find that the new property will not cash flow but you run a significant surplus on the prior property then the portfolio may cash flow.
Figure you need between 1.25 and 1.50 for a debt service multiple. The income projected needs to be 1.25 times the monthly mortgage payment at a minimum is how you apply the ratio. If you really want to speculate that prices will rise long term yet the cash flow is not there to cover everything and a buffer then 'buy' a larger buffer. This means taking a lump sum of cash and setting it aside to fund the gaps. The gaps are real and they do happen. Note that 'buying' the buffer is really a conservative way to speculate on appreciation rather than have the tenant pay for your speculation.
I have been investing for over 20 years in the property sector. Multiple countries no less. Rather than focus on the doom and gloom a long term investor looks at the fundamentals (mostly the cash flow). If there is cash flow then there is someone else paying to keep you in the game. If they really are paying enough to cover all costs and all reserves you just sit back and let the market come to you if and when it does. If the market was never to appreciate (no doom and gloomer will argue this point) you likely will still see rents rise. The logic is people who have jobs expect that over 10 or 20 years their pay will rise. Rents tend to move at the same time broadly speaking. People figure that paying up to 1/3 of their income for housing is reasonable (3.5 times 1 person's income). Hence long term rises in employment and income levels translate into long term rent and housing price rises.
BTW - If you buy in an area that has a lack or jobs and no future prospects the logic still applies. I am saying there is a connection between income levels and rising employment that over long periods is even more important than short term interest rates.
John Corey