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The short answer: usually more than 20% equity. Lenders cap your combined loan-to-value around 80–85%, and they won't let you borrow down to zero equity, so you need a buffer.
A worked example
Home worth $400,000, mortgage of $300,000. That's $100,000 of equity (a 75% LTV). At an 85% CLTV cap, total debt can reach $340,000, leaving about $40,000 of HELOC room. If you only had 10% equity, there'd be nothing to draw.
Run your own figures on the home equity calculator.