Paste gtm wideip and gtm pool stanzas (as tmsh list gtm wideip a <name> and tmsh list gtm pool a <name> print them) and the two-tier BIG-IP DNS (formerly GTM - Global Traffic Manager) decision renders as it really runs.
The wide-IP tier shows the pool-selection method (pool-lb-mode, default round-robin) with the attached pools, their order and ratio values, and the wide-IP settings that shape answers: persistence, last-resort-pool, failure-rcode behavior, and the decision-log verbosity knob that lets you watch this same flow in the logs.
The pool tier renders the three-step chain: preferred (load-balancing-mode), alternate (alternate-mode), fallback (fallback-mode), each step carrying the vendor's semantics for the tier and the method. The defaults are applied and labeled when an attribute is absent: round-robin, round-robin, return-to-dns.
Underneath, deterministic observations cross-check the configuration against the documented grammar and the Load Balancing manual's rules: methods outside a tier's admitted token list, the fallback tier's ignores-availability property stated on every resolved chain, Fallback IP wiring (the method with no address, or an address no tier uses), the dynamic-ratio applicability set, zeroed QoS coefficients, member ratios no tier consumes, the Global Availability pairing rule, and the topology-at-both-tiers warning that wants each pool's fallback set to None.
A single method name explains that one method, including which tiers admit it and where its decision signal comes from (LDNS-path probing, server-side statistics, or none). The word methods lists both catalogues.
Everything runs locally; nothing you paste leaves the page.