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Following the recent evidence for a gravitational wave (GW) background found by pulsar timing array (PTA) experiments, the next major science milestone is resolving individual supermassive black hole binaries (SMBHBs). The detection of these systems could arise via searches using a power-based GW anisotropy model, i.e., a cross-correlation search for single sources, or a deterministic template model. In Schult et al. [Expectations for the first supermassive black-hole binary resolved by PTAs. I. Model efficacy, Phys. Rev. D 114, 023034 (2026).PRVDAQ2470-001010.1103/vncm-5j2n], we compared the efficacy of these models in constraining the GW signal from a single SMBHB using realistic, near-future PTA datasets, and found that the full-signal deterministic continuous wave (CW) search may achieve detection and characterization first. Here, we continue our analyses using only the CW model given its better performance, focusing now on characterization milestones. We examine the order in which CW parameters are constrained as PTA data are accumulated and the signal-to-noise ratio (<inline-formula><mml:math><mml:mrow><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></inline-formula>) grows. We also study how these parameter constraints vary across sources of different sky locations and GW frequencies. We find that the GW frequency and strain are generally constrained at the same time (or <inline-formula><mml:math><mml:mrow><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></inline-formula>), closely followed by the sky location, and later the chirp mass (if the source is highly evolving) and inclination angle. At fixed <inline-formula><mml:math><mml:mrow><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></inline-formula>, sources at higher frequencies generally achieve better precision on the GW frequency, chirp mass, and sky location. The time (and <inline-formula><mml:math><mml:mrow><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></inline-formula>) at which the signal becomes constrained is dependent on the sky location and frequency of the source, with the effects of pulsar terms and PTA geometry playing crucial roles in source detection and localization.

One of the most promising targets for pulsar timing arrays (PTAs) is identifying an individual supermassive black hole binary (SMBHB) out of the population of binaries theorized to produce a gravitational wave background (GWB). In this work, we emulate an evolving PTA dataset, complete with an increasing number of pulsars and timing baselines, into which we inject a single binary on top of a Gaussian GWB signal. We vary the binary's source parameters, including sky position and frequency, and create ten noise realizations for each source/PTA combination to synthesize an ensemble of simulated datasets with which we assess current Bayesian binary search techniques. We develop a novel, cross-correlation based model tuned for individual SMBHBs and compare its binary detection and characterization capabilities to two waveform-based template models. This spike pixel (SP) technique is designed to identify the frequency-specific anisotropy induced by an individual SMBHB. We find that a template-based search, including the full gravitational wave signal structure (i.e., both the Earth and pulsar effects of an incident GW) returns the highest Bayes factors (BF) and has the most robust parameter estimations. SP attains a realization-median <inline-formula><mml:math><mml:mrow><mml:mi>BF</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math></inline-formula> at source strengths <inline-formula><mml:math><mml:mrow><mml:mn>7</mml:mn><mml:mo>&lt;</mml:mo><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mo>&lt;</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:math></inline-formula>. Interestingly, despite being a deterministic model, the Earth-term template struggles to identify and characterize low-frequency binaries (i.e., at 5 nHz). These binaries require higher source strengths (<inline-formula><mml:math><mml:mrow><mml:mn>16</mml:mn><mml:mo>&lt;</mml:mo><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mo>&lt;</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:math></inline-formula>) to reach the same BF threshold. This is likely due to neglected confusion effects between the pulsar and Earth terms. By contrast, the SP shows promise for parameter estimation despite treating a binary's GW signal as excess directional GW power without phase modeling. Sky location and frequency parameter constraints returned by the SP are only surpassed by the Earth-term template model at <inline-formula><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mo>∼</mml:mo><mml:mn>12</mml:mn><mml:mi>─</mml:mi><mml:mn>13</mml:mn></mml:mrow></mml:math></inline-formula>. Milestones for a first detection using the full-signal GW model are included in a following paper, Petrov et al. [Expectations for the first supermassive black-hole binary resolved by PTAs. II. Milestones for binary characterization, Phys Rev. D 114, 023033 (2026).10.1103/zp2x-r4mp].