"Would" is a modal and modals take the bare infinitive after them. You are misreading the sentence if you interpret "climb" and "stare" as present tense -- they are bare infinitives.
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AnonymousDoes anybody here know of a rule that doesn't involve looking at "would" as a conditional?Yes. It's the rule that governs all modal verbs regardless of their use or meaning. A modal verb must be followed by a base form (that is, a bare infinitive). Always.