Possible Clues:

• Tap, as savings
• Take a little bit from
• Spend some of
• Take a bit from, as savings
• Help oneself, being keen on chasing pickpocket
• Take cursory interest in girl on horse
• Digging underneath sink to find tap
• Casually read detective novel (part two) after some beer
• Detective takes horse to look at briefly
• Make use of (one's financial resources)